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Edit made on November 23, 2008 by DerekCouzens at 20:05:39
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A group A is a set, combined with a binary operation *, which has 4 specific properties.
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* Closure:
* Associativity:
* Identity:
* Inverse:
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The set A is closed
The operation * is associative. (see associative operation)
The operation * is associative.
A contains an identity element.
For every element in A there exists an inverse element
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These are called the group axioms.
If the binary operation is also commutative i.e. a * b = b * a then the group is called an Abelian Group or commutative group.
If the binary operation is also commutative (see commutative operation) then the group is called an Abelian Group or commutative group.