## 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.

Last updated: 1998-10-03

### Nearby terms:

grok ♦ gronk ♦ gronked ♦ **group** ♦ Group 3 ♦ Group 4 ♦ Group Code Recording

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