A group is a non empty set G with a binary operation, * defined on it and so that the following axioms hold. G1: a *(b*c) = (a*b)*c for all a, b, c in G G2: there is an element 1 in G such that 1*a = a*1 = a for all in a in G G3: for every element a in G, there is an element a-1 in G such that a*a-1 = 1 = a-1*a Any group is an abelian group if for a, b in G then a*b = b*a. it is very common to write abelian group operations with additive operation because many of the groups arise from additive ...
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