Difference between revisions of "Group (mathematics)"
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A group with commutative binary operator is known as [[Abelian group|Abelian]]. | A group with commutative binary operator is known as [[Abelian group|Abelian]]. | ||
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Revision as of 09:00, March 27, 2007
A group is a set of elements combined with a binary operator which satisfies four conditions:
- Closure: applying the binary operator to any two elements of the group produces a result which itself belongs to the group
- Associativity:
where 
, 
and 
are any element of the group - Existence of Identity: there must exist an identity element
such that 
; that is, applying the binary operator to some element and the identity element leaves unchanged - Existence of Inverse: for each element , there must exist an inverse
such that 
A group with commutative binary operator is known as Abelian.
