On the set of natural numbers which only yield orders of Abelian groups
type: Item
instance of: scholarly article
title: On the set of natural numbers which only yield orders of Abelian groups
zbMATH Open document ID: 0576.10031
DOI: 10.1016/0022-314X(85)90026-5
author: Richard Warlimont
published in: Journal of Number Theory
publication date: 1985-01-01T00:00:00Z
review text: 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 \[ x(\log \log x)^{-1}\ll f(x)\ll x(\log \log x)^{-1}(\log \log \log x\quad)^{c-1/2}. \]
Mathematics Subject Classification ID: 11N37
Mathematics Subject Classification ID: 20K01
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 3920590
zbMATH Keywords: Abelian groups
zbMATH Keywords: multiplicative functions
reviewed by: Władysław Narkiewicz
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3920590