Difference between revisions of "Abelian group"
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For a [[group]] to be considered "abelian", it must meet several requirements. | For a [[group]] to be considered "abelian", it must meet several requirements. | ||
| − | + | Closure | |
| − | For all <math>a,b</math> <math>\in</math> <math>S</math>, and for all | + | For all <math>a,b</math> <math>\in</math> <math>S</math>, and for all operations <math>\bullet</math>, <math>a\bullet b \in S</math>. |
| + | Associativity | ||
| + | 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>. | ||
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{{stub}} | {{stub}} | ||
Revision as of 17:31, 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
.
.
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