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Новая страница: «Taken from [http://en.wikipedia.org/wiki/Template:Group-like_structures] {| style="text-align:center" |- align="center" | style="border-bottom: 2px solid #303060"...»
Taken from [http://en.wikipedia.org/wiki/Template:Group-like_structures]
{| style="text-align:center"
|- align="center"
| style="border-bottom: 2px solid #303060" colspan=6| '''Group-like structures'''
|-
! !! [[Total Function|Totality]]* !! [[Associativity]] !! [[Identity element|Identity]] !! [[Inverse element|Inverses]] !! [[Commutativity]]
|-
! [[Magma (algebra)|Magma]]
| Y || N || N || N || N
|-
! [[Semigroup]]
| Y || Y || N || N || N
|-
! [[Monoid]]
| Y || Y || Y || N || N
|-
! [[Group (mathematics)|Group]]
| Y || Y || Y || Y || N
|-
! [[Abelian Group]]
| Y || Y || Y || Y || Y
|-
! [[Loop (algebra)|Loop]]
| Y || N || Y || Y** || N
|-
! [[Quasigroup]]
| Y || N || N || N || N
|-
! [[Groupoid]]
| N || Y || Y || Y || N
|-
! [[Category (mathematics)|Category]]
| N || Y || Y || N || N
|-
! [[Semicategory]]
| N || Y || N || N || N
|-
| || colspan="5" | <small>*[[Closure (mathematics)|Closure]], which is used in many sources to define group-like structures, is an equivalent axiom to totality, though defined differently.</small>
|-
| || colspan="5" | <small>**Each element of a [[Loop (algebra)|loop]] has a left and right inverse, but these need not coincide.</small>
|}
{| style="text-align:center"
|- align="center"
| style="border-bottom: 2px solid #303060" colspan=6| '''Group-like structures'''
|-
! !! [[Total Function|Totality]]* !! [[Associativity]] !! [[Identity element|Identity]] !! [[Inverse element|Inverses]] !! [[Commutativity]]
|-
! [[Magma (algebra)|Magma]]
| Y || N || N || N || N
|-
! [[Semigroup]]
| Y || Y || N || N || N
|-
! [[Monoid]]
| Y || Y || Y || N || N
|-
! [[Group (mathematics)|Group]]
| Y || Y || Y || Y || N
|-
! [[Abelian Group]]
| Y || Y || Y || Y || Y
|-
! [[Loop (algebra)|Loop]]
| Y || N || Y || Y** || N
|-
! [[Quasigroup]]
| Y || N || N || N || N
|-
! [[Groupoid]]
| N || Y || Y || Y || N
|-
! [[Category (mathematics)|Category]]
| N || Y || Y || N || N
|-
! [[Semicategory]]
| N || Y || N || N || N
|-
| || colspan="5" | <small>*[[Closure (mathematics)|Closure]], which is used in many sources to define group-like structures, is an equivalent axiom to totality, though defined differently.</small>
|-
| || colspan="5" | <small>**Each element of a [[Loop (algebra)|loop]] has a left and right inverse, but these need not coincide.</small>
|}
