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A group A is a set, combined with a binary operation *, which has 4 specific properties.
The set A is closed

The operation * is associative.

A contains an identity element.

For every element in A there exists an inverse element

These are called the group axioms.

If the binary operation is also commutative (see commutative operation) then the group is called an Abelian Group or commutative group.

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