group

A group G is a non-empty set upon which a binary operator

* is defined with the following properties for all a,b,c in G:

Closure: G is closed under *, a*b in G

Associative: * is associative on G, (a*b)*c = a*(b*c)

Identity: There is an identity element e such that

a*e = e*a = a.

Inverse: Every element has a unique inverse a' such that

a * a' = a' * a = e. The inverse is usually

written with a superscript -1.

(1998-10-03)