Abelian group

Revision as of 18:34, 12 August 2015 by Pi3point14 (talk | contribs)

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 $a,b$ $\in$ $S$, and for all operations $\bullet$, $a\bullet b \in S$.

Associativity

         For all $a,b,c$ $\in$ $S$ and all operations $\bullet$, $(a\bullet b)\bullet c=a\bullet(b\bullet c)$.

Identity Element

         There exists some $e \in S$ such that $a\bullete=e\bullleta=a$ (Error compiling LaTeX. Unknown error_msg).


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