Изменения

Перейти к: навигация, поиск

Конечная группа

28 527 байт убрано, 01:45, 16 сентября 2010
Нет описания правки
=== Примеры таблиц умножения для конечных групп ===
Ниже перечислены все группы до шестого порядка включительно:
 
1) n = 1
{| border="1" cellpadding="4" align="center"
2) n = 2
{| border="1" cellpadding="4" align="center"
| <tex>\mathbb{Z}_2</tex>|-!style="background:#efefef;"| *+!style="background:#efefef;"| <big>e0</big> !style="background:#efefef;"| <big>a1</big>
|-
!style="background:#efefef;"| <big>e0</big>| <big>e0</big> || <big>a1</big>
|-
!style="background:#efefef;"| <big>a1</big>| <big>a1</big> || <big>e0</big>
|}
3) n = 3
{| border="1" cellpadding="4" align="center"
| <tex>\mathbb{Z}_3</tex>|-!style="background:#efefef;"| *+!style="background:#efefef;"| <big>e0</big> !style="background:#efefef;"| <big>a1</big> !style="background:#efefef;"| <big>b2</big>
|-
!style="background:#efefef;"| <big>e0</big>| <big>e0</big> || <big>a1</big> || <big>b2</big>
|-
!style="background:#efefef;"| <big>a1</big>| <big>a1</big> || <big>b2</big> || <big>e0</big>
|-
!style="background:#efefef;"| <big>b2</big>| <big>b2</big> || <big>e0</big> || <big>a1</big>
|}
4) n = 4
{| border="1" cellpadding="4" align="center"
!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big> !style="background:#efefef;"| <big>a</big> !style="background:#efefef;"| <big>b</big> !style="background:#efefef;"| <big>c</big> |-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big>|-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>e</big> || <big>c</big> || <bigtex>b\mathbb{Z}_2</bigtex>
|-
!style="background:#efefef;"| <big>b</big>+!style="background:#efefef;"| <big>b0</big> |!style="background:#efefef;"| <big>c1</big> |!style="background:#efefef;"| <big>e2</big> |!style="background:#efefef;"| <big>a3</big>
|-
!style="background:#efefef;"| <big>c0</big>| <big>c0</big> || <big>b</big> || <big>a1</big> || <big>e2</big>|} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big> !style="background:#efefef;"| <big>a</big> !style="background:#efefef;"| <big>b</big> !style="background:#efefef;"| <big>c3</big>
|-
!style="background:#efefef;"| <big>e1</big>| <big>e1</big> || <big>a0</big> || <big>b3</big> || <big>c2</big>
|-
!style="background:#efefef;"| <big>a2</big>| <big>a2</big> || <big>b3</big> || <big>c0</big> || <big>e</big>|-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>e</big> || <big>a1</big>
|-
!style="background:#efefef;"| <big>c3</big>| <big>c3</big> || <big>e2</big> || <big>a1</big> || <big>b0</big>
|}
{| border="1" cellpadding="4" align="center"
!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big> !style="background:#efefef;"| <big>a</big> !style="background:#efefef;"| <big>b</big> !style="background:#efefef;"| <bigtex>c\mathbb{Z}_2\times\mathbb{Z}_2</bigtex>
|-
!style="background:#efefef;"| <big>e</big>+!style="background:#efefef;"| <big>e(0,0)</big> |!style="background:#efefef;"| <big>a(0,1)</big> |!style="background:#efefef;"| <big>b(1,0)</big> |!style="background:#efefef;"| <big>c(1,1)</big>
|-
!style="background:#efefef;"| <big>a(0,0)</big>| <big>a(0,0)</big> || <big>e(0,1)</big> || <big>c(1,0)</big> || <big>b(1,1)</big>
|-
!style="background:#efefef;"| <big>b(0,1)</big>| <big>b(0,1)</big> || <big>c(0,0)</big> || <big>a(1,1)</big> || <big>e(1,0)</big>
|-
!style="background:#efefef;"| <big>c(1,0)</big>| <big>c(1,0)</big> || <big>b(1,1)</big> || <big>e(0,0)</big> || <big>a</big>|}5(0,1) n = 5{| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big> !style="background:#efefef;"| <big>a</big> !style="background:#efefef;"| <big>b</big> !style="background:#efefef;"| <big>c</big> !style="background:#efefef;"| <big>d</big> |-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big>
|-
!style="background:#efefef;"| <big>a(1,1)</big>| <big>a(1,1)</big> || <big>b(1,0)</big> || <big>c(0,1)</big> || <big>d</big> || <big>e</big>|-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>d</big> || <big>e</big> || <big>a</big>|-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>d</big> || <big>e</big> || <big>a</big> || <big>b</big>|-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>e</big> || <big>a</big> || <big>b</big> || <big>c(0,0)</big>
|}
65) n = 65
{| border="1" cellpadding="4" align="center"
!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <bigtex>f\mathbb{Z}_2</bigtex>
|-
!style="background:#efefef;"| <big>e</big>+!style="background:#efefef;"| <big>e0</big> |!style="background:#efefef;"| <big>a1</big> |!style="background:#efefef;"| <big>b2</big> |!style="background:#efefef;"| <big>c3</big> || <big>d</big> |!style="background:#efefef;"| <big>f4</big>
|-
!style="background:#efefef;"| <big>a0</big>| <big>a0</big> || <big>e1</big> || <big>c2</big> || <big>b3</big> || <big>f</big> || <big>d4</big>
|-
!style="background:#efefef;"| <big>b1</big>| <big>b1</big> || <big>c2</big> || <big>d3</big> || <big>f4</big> || <big>e</big> || <big>a0</big>
|-
!style="background:#efefef;"| <big>c2</big>| <big>c2</big> || <big>b3</big> || <big>f4</big> || <big>d0</big> || <big>a</big> || <big>e1</big>
|-
!style="background:#efefef;"| <big>d3</big>| <big>d3</big> || <big>f4</big> || <big>e0</big> || <big>a1</big> || <big>b</big> || <big>c2</big>
|-
!style="background:#efefef;"| <big>f4</big>| <big>f4</big> || <big>d0</big> || <big>a1</big> || <big>e2</big> || <big>c</big> || <big>b3</big>
|}
{| border6) n ="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>e</big> || <big>c</big> || <big>d</big> || <big>f</big> || <big>b</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> || <big>e</big> || <big>a</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>b</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>d</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>e</big> |}6
{| border="1" cellpadding="4" align="center"
!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <bigtex>f\mathbb{Z}_6</bigtex>
|-
!style="background:#efefef;"| <big>e</big>+!style="background:#efefef;"| <big>e0</big> |!style="background:#efefef;"| <big>a1</big> |!style="background:#efefef;"| <big>b2</big> |!style="background:#efefef;"| <big>c3</big> |!style="background:#efefef;"| <big>d4</big> |!style="background:#efefef;"| <big>f5</big>
|-
!style="background:#efefef;"| <big>a0</big>| <big>a0</big> || <big>e1</big> || <big>c2</big> || <big>b3</big> || <big>f4</big> || <big>d5</big>
|-
!style="background:#efefef;"| <big>b1</big>| <big>b1</big> || <big>c2</big> || <big>d3</big> || <big>f4</big> || <big>a5</big> || <big>e0</big>
|-
!style="background:#efefef;"| <big>c2</big>| <big>c2</big> || <big>b3</big> || <big>f4</big> || <big>d5</big> || <big>e0</big> || <big>a1</big>
|-
!style="background:#efefef;"| <big>d3</big>| <big>d3</big> || <big>f4</big> || <big>a5</big> || <big>e0</big> || <big>b1</big> || <big>c2</big>
|-
!style="background:#efefef;"| <big>f4</big>| <big>f</big> || <big>d</big> || <big>e4</big> || <big>a5</big> || <big>c0</big> || <big>b</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c2</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f3</big>
|-
!style="background:#efefef;"| <big>e5</big>| <big>e5</big> || <big>a0</big> || <big>b1</big> || <big>c2</big> || <big>d3</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>e</big> || <big>c</big> || <big>f</big> || <big>b</big> || <big>d</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>f</big> || <big>d</big> || <big>a</big> || <big>e</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>b</big> || <big>d</big> || <big>e</big> || <big>f</big> || <big>a</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>e</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>e</big> || <big>a</big> || <big>c</big> || <big>b4</big>
|}
{| border="1" cellpadding="4" align="center"
!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>e</big> || <big>d</big> || <big>b</big> || <big>f</big> || <big>c</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>e</big> || <big>f</big> || <big>a</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>b</big> || <big>f</big> || <big>d</big> || <big>e</big> || <big>a</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>a</big> || <big>e</big> || <big>c</big> || <bigtex>b\mathbb{S}_3</bigtex>
|-
!style="background:#efefef;"| <big>f</big>
| <big>f</big> || <big>d</big> || <big>c</big> || <big>a</big> || <big>b</big> || <big>e</big>
|}
 
{| border="1" cellpadding="4" align="center"
!style="background:#efefef;"| *
!style="background:#efefef;"| <big>e</big>
!style="background:#efefef;"| <big>a</big>
!style="background:#efefef;"| <big>aa</big>
!style="background:#efefef;"| <big>b</big>
!style="background:#efefef;"| <big>c</big>
!style="background:#efefef;"| <big>d</big>
!style="background:#efefef;"| <big>f</big>
|-
!style="background:#efefef;"| <big>e</big>
| <big>e</big> || <big>a</big> || <big>baa</big> || <big>cb</big> || <big>dc</big> || <big>fd</big>
|-
!style="background:#efefef;"| <big>a</big>
| <big>a</big> || <big>eaa</big> || <big>de</big> || <big>fc</big> || <big>cd</big> || <big>b</big>
|-
!style="background:#efefef;"| <big>baa</big>| <big>b</big> || <big>c</big> || <big>e</big> || <big>a</big> || <big>f</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>b</big> || <big>f</big> || <big>d</big> || <big>aaa</big> || <big>e</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>e</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>c</big> || <big>e</big> || <big>b</big> || <big>a</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>b</big> || <big>c</big>
|-
!style="background:#efefef;"| <big>b</big>
| <big>b</big> || <big>cd</big> || <big>ec</big> || <big>de</big> || <big>faa</big> || <big>a</big>
|-
!style="background:#efefef;"| <big>c</big>
| <big>c</big> || <big>b</big> || <big>fd</big> || <big>ea</big> || <big>ae</big> || <big>daa</big>
|-
!style="background:#efefef;"| <big>d</big>
| <big>d</big> || <big>f</big> || <big>ac</big> || <big>b</big> || <big>c</big> || <big>e</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>caa</big> || <big>a</big> || <big>e</big> || <big>b</big>
|}
{| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>c</big> || <big>b</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>a</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>b</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>d</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>e</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>c</big> || <big>a</big> || <big>b</big> || <big>e</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>b</big> || <big>c</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>b</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>a</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>e</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>c</big> || <big>a</big> || <big>e</big> || <big>b</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>c</big> || <big>b</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>b</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>a</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>e</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>c</big> || <big>a</big> || <big>b</big> || <big>e</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>c</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>e</big> || <big>a</big> || <big>f</big> || <big>c</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>d</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>b</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>c</big> || <big>a</big> || <big>b</big> || <big>e</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>c</big> || <big>d</big> || <big>b</big> || <big>e</big> || <big>a</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>c</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>e</big> || <big>a</big> || <big>f</big> || <big>c</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>d</big> || <big>f</big> || <big>e</big> || <big>b</big> || <big>a</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>c</big> || <big>a</big> || <big>e</big> || <big>b</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>c</big> || <big>d</big> || <big>b</big> || <big>a</big> || <big>e</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>c</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>e</big> || <big>a</big> || <big>f</big> || <big>c</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>d</big> || <big>f</big> || <big>a</big> || <big>e</big> || <big>b</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>c</big> || <big>e</big> || <big>b</big> || <big>a</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>c</big> || <big>d</big> || <big>b</big> || <big>a</big> || <big>e</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>c</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>e</big> || <big>a</big> || <big>f</big> || <big>c</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>d</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>e</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>c</big> || <big>b</big> || <big>e</big> || <big>a</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>c</big> || <big>d</big> || <big>e</big> || <big>a</big> || <big>b</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>c</big> || <big>e</big> || <big>f</big> || <big>d</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>cДля группы </bigtex> || <big>d</big> || <big>f</big> || <big>e</big> || <big>a</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>e</big> || <big>f</big> || <big>d</big> || <big>a</big> || <big>b</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>e</big> |} \mathbb{| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>c</big> || <big>e</big> || <big>f</big> || <big>d</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> || <big>a</big> || <big>e</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>e</big> || <big>f</big> || <big>d</big> || <big>b</big> || <big>a</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>e</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>e</big> || <big>a</big> || <big>c</big> || <big>b</big> |S{| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e_3</bigtex>!style="background:#efefef;"| <bigtex>a</bigtex>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| это циклическая перестановка <bigtex>e(123)\rightarrow(231)</bigtex>| , а <big>e</big> || <big>a</big> || <bigtex>b</big> || <big>,\,c</big> || <big>,\,d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>d</big> || <big>e</big> || <big>f</big> || <big>c</bigtex> |-!style="background:#efefef;"| транспозиции <bigtex>b(123)\rightarrow(213),\,(123)\rightarrow(132),\,(123)\rightarrow(321)</bigtex>| <big>b</big> || <big>c</big> || <big>e</big> || <big>f</big> || <big>a</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>e</big> || <big>f</big> || <big>d</big> || <big>b</big> || <big>a</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>e</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>c</big> || <big>a</big> || <big>e</big> || <big>b</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>d</big> || <big>e</big> || <big>f</big> || <big>c</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>e</big> || <big>f</big> || <big>a</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>e</big> || <big>f</big> || <big>d</big> || <big>b</big> || <big>a</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>c</big> || <big>a</big> || <big>e</big> || <big>b</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>e</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> || <big>e</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>e</big> || <big>f</big> || <big>a</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>d</big> || <big>f</big> || <big>e</big> || <big>b</big> || <big>a</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>e</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>e</big> || <big>d</big> || <big>a</big> || <big>c</big> || <big>b</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> || <big>e</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>e</big> || <big>f</big> || <big>a</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>d</big> || <big>f</big> || <big>a</big> || <big>e</big> || <big>b</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>a</big> || <big>e</big> || <big>b</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>e</big> || <big>d</big> || <big>b</big> || <big>c</big> || <big>a</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> || <big>e</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>a</big> || <big>f</big> || <big>e</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>d</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>b</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>e</big> || <big>d</big> || <big>b</big> || <big>c</big> || <big>a</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> || <big>e</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>f</big> || <big>e</big> || <big>a</big> || <big>d</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>d</big> || <big>e</big> || <big>f</big> || <big>b</big> || <big>a</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>e</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>e</big> || <big>d</big> || <big>a</big> || <big>c</big> || <big>b</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>c</big> || <big>f</big> || <big>e</big> || <big>d</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>a</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>f</big> || <big>d</big> || <big>e</big> || <big>a</big> || <big>b</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>e</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>e</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>c</big> || <big>f</big> || <big>e</big> || <big>d</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>e</big> || <big>d</big> || <big>f</big> || <big>a</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>f</big> || <big>d</big> || <big>a</big> || <big>b</big> || <big>e</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>e</big> || <big>f</big> || <big>b</big> || <big>a</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>a</big> || <big>e</big> || <big>c</big> || <big>b</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>c</big> || <big>f</big> || <big>e</big> || <big>d</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>a</big> || <big>d</big> || <big>f</big> || <big>e</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>f</big> || <big>d</big> || <big>e</big> || <big>a</big> || <big>b</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>e</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>e</big> || <big>b</big> || <big>c</big> || <big>a</big> |} {| border="1" cellpadding="4" align="center"!style="background:#efefef;"| *!style="background:#efefef;"| <big>e</big>!style="background:#efefef;"| <big>a</big>!style="background:#efefef;"| <big>b</big>!style="background:#efefef;"| <big>c</big>!style="background:#efefef;"| <big>d</big>!style="background:#efefef;"| <big>f</big>|-!style="background:#efefef;"| <big>e</big>| <big>e</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>d</big> || <big>f</big> |-!style="background:#efefef;"| <big>a</big>| <big>a</big> || <big>b</big> || <big>c</big> || <big>f</big> || <big>e</big> || <big>d</big> |-!style="background:#efefef;"| <big>b</big>| <big>b</big> || <big>c</big> || <big>d</big> || <big>e</big> || <big>f</big> || <big>a</big> |-!style="background:#efefef;"| <big>c</big>| <big>c</big> || <big>f</big> || <big>e</big> || <big>d</big> || <big>a</big> || <big>b</big> |-!style="background:#efefef;"| <big>d</big>| <big>d</big> || <big>e</big> || <big>f</big> || <big>a</big> || <big>b</big> || <big>c</big> |-!style="background:#efefef;"| <big>f</big>| <big>f</big> || <big>d</big> || <big>a</big> || <big>b</big> || <big>c</big> || <big>e</big> |} соответственно.
[[Категория: Теория групп]]
Анонимный участник

Навигация