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On the set of natural numbers which only yield orders of Abelian groups. (English) Zbl 0576.10031

It is shown that if f(x) is the number of integers \(n\leq x\) such that all groups of order n are Abelian and there are at least two of them, then for every positive c one has \[ x(\log \log x)^{-1}\ll f(x)\ll x(\log \log x)^{-1}(\log \log \log x\quad)^{c-1/2}. \]
Reviewer: W.Narkiewicz

MSC:

11N37 Asymptotic results on arithmetic functions
20K01 Finite abelian groups
20D60 Arithmetic and combinatorial problems involving abstract finite groups
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