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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