Let f1(n) denote the number of abelian groups of order n and f2(n) the number of semi-simple rings with n elements. What can be said about the magnitude of fi(n)? We shall prove that one can expect, on the average, about 2.3 groups and 2.5 rings of the kind stated for a given order. First we state without proof the two relevant structure theorems (which are readily available in standard texts).
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