On the Density of Various Classes of Groups
نویسندگان
چکیده
Let B be a subset of the set of all isomorphism classes of finite groups. We consider the number Fg(x) of positive integers n < x such that all groups of order n lie in B. When ir consists of the isomorphism classes of all finite groups of any of the following types, we obtain an asymptotic formula for Fn(x): cyclic groups, abelian groups, nilpotent groups, supersolvable groups, and solvable groups. In the course of the arguments, we also obtain, for almost all n, a lower bound for the number of groups of a given order n.
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