Minimal Abelian automorphism groups of finite groups
type: Item
instance of: scholarly article
title: Minimal Abelian automorphism groups of finite groups
zbMATH Open document ID: 0846.20024
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1996-09-25T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108365
review text: The main result of the paper is the following: Let \(G\) be a finite non-cyclic \(p\)-group, \(p\) odd, for which \(\text{Aut }G\) is Abelian. Then \(p^{12}\) divides \(\text{Aut }G\). This is the best possible lower bound, as \textit{M. Morigi} [Rend. Semin. Mat. Univ. Padova 92, 47-58 (1994; Zbl 0829.20028)] constructed groups \(G\) of order \(p^7\) with \(\text{Aut }G\) Abelian of order \(p^{12}\). For \(p=2\) the minimal order of an Abelian automorphism group of a finite 2-group is 128, for a group of order 64 found by G. A. Miller in 1913.
Mathematics Subject Classification ID: 20D45
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 889835
zbMATH Keywords: finite non-cyclic \(p\)-groups
zbMATH Keywords: minimal order
zbMATH Keywords: Abelian automorphism groups
zbMATH Keywords: finite 2-groups
author: Peter Hegarty
reviewed by: Péter P. Pálfy
MaRDI profile type: Publication
cites work: Automorphisms of a \(p\)-group
cites work: Q5534298
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cites work: Q4881241
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cites work: Q4881268
cites work: On \(p\)-groups with abelian automorphism group
cites work: The Central Automorphisms of a Finite Group
description: scientific article; zbMATH DE number 889835