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Groups

Groups

A pair (G, *) where G is a non- empty set * a binary operation in G is a group if and only if

(1) The binary operation * closed a *b=b* a a, b belong to G

(2) The binary operation * is associative   (a*b)*c= a*(b*c)

(3) There is an identity element e belong to G, such that for all a belong to G a* e= e* a=a

(4) For each a belong to G there is element a`  belong to G such that a* a`=a`*a= e where a` is called the inverse of a in G

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