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.

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