Minimal Abelian groups that are not automorphism groups
type: Item
instance of: scholarly article
title: Minimal Abelian groups that are not automorphism groups
zbMATH Open document ID: 0910.20016
author: Guining Ban
author: ShuXia Yu
published in: Archiv der Mathematik
publication date: 1999-02-09T00:00:00Z
review text: This paper deals with abelian \(p\)-groups of minimal order which can occur as the automorphism group of a finite group. In particular the authors prove that if \(G\) is a non-cyclic group of order \(p^7\) and \(\Aut G\) is abelian, then \(\Aut G\) must be of order \(p^{12}\). Moreover, there is no group \(G\) such that \(\Aut G\) is an abelian \(p\)-group of order \(p^{11}\) (where \(p>2\)).
Mathematics Subject Classification ID: 20D45
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20F29
zbMATH DE Number: 1186698
zbMATH Keywords: automorphism groups
zbMATH Keywords: Abelian \(p\)-groups
zbMATH Keywords: finite groups
reviewed by: Silvana Franciosi
MaRDI profile type: Publication
full work available at URL: s000130050215
OpenAlex ID: W2078280577
DOI: 10.1007/S000130050215
description: scientific article; zbMATH DE number 1186698