Difference between revisions of "Abelian group"
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For all <math>a,b,c</math> <math>\in</math> <math>S</math> and all operations <math>\bullet</math>, <math>(a\bullet b)\bullet c=a\bullet(b\bullet c)</math>. | For all <math>a,b,c</math> <math>\in</math> <math>S</math> and all operations <math>\bullet</math>, <math>(a\bullet b)\bullet c=a\bullet(b\bullet c)</math>. | ||
Identity Element | Identity Element | ||
| − | There exists some <math>e \in S</math> such that <math>a \bullet e = e \bullet a | + | There exists some <math>e \in S</math> such that <math>a \bullet e = e \bullet a = a</math>. |
Revision as of 17:36, 12 August 2015
An abelian group is a group in which the group operation is commutative. For a group to be considered "abelian", it must meet several requirements.
Closure
For all
, and for all operations
,
.
, and for all operations 
, 
.
Associativity
For all
.
.
Identity Element
There exists somesuch that
.
such that 
.
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