On \(p\)-groups with abelian automorphism group
type: Item
instance of: scholarly article
title: On \(p\)-groups with abelian automorphism group
zbMATH Open document ID: 0829.20028
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1996-01-16T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108342
review text: In 1913 Miller has shown that there exists a group of order \(2^6\) whose automorphism group is abelian. Here it is shown, that for an odd prime \(p\) no finite non-cyclic \(p\)-group of order \(p^6\) with abelian automorphism group exists. On the other hand, an example of a finite \(p\)- group of order \(p^7\) is given whose automorphism group is abelian. This group is special, is generated by 4 elements, and is the smallest of an infinite family of groups of order \(p^{n^2+3n+3}\), where \(n\) is a natural number.
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20D45
Mathematics Subject Classification ID: 20F28
zbMATH DE Number: 763291
zbMATH Keywords: Abelian automorphism groups
zbMATH Keywords: finite \(p\)-groups
author: Marta Morigi
reviewed by: Bernhard Amberg
MaRDI profile type: Publication
cites work: The occurrence of finite groups in the automorphism group of nilpotent groups of class 2
cites work: Endliche Gruppen I
cites work: Some non-abelian p-groups with abelian automorphism groups
cites work: The Central Automorphisms of a Finite Group
description: scientific article; zbMATH DE number 763291