## Most recent change of Group

Edit made on November 23, 2008 by DerekCouzens at 20:05:39

Deleted text in red /
Inserted text in green

WW

HEADERS_END

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

COLUMN_START^

* Closure:

* Associativity:

* Identity:

* Inverse:

COLUMN_SPLIT^

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

COLUMN_END

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.