Difference between revisions of "Abelian group"
Pi3point14 (talk | contribs) |
Pi3point14 (talk | contribs) |
||
| Line 6: | Line 6: | ||
Associativity | 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>. | 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 | |
| + | There exists some <math>e \in S</math> such that <math>a\bullete=e\bullleta=a</math>. | ||
Revision as of 18:34, 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 $a\bullete=e\bullleta=a$ (Error compiling LaTeX. Unknown error_msg).
such that
This article is a stub. Help us out by expanding it.
