A result about Abelian automorphism groups
type: Item
instance of: scholarly article
title: A result about Abelian automorphism groups
zbMATH Open document ID: 0886.20015
DOI: 10.1007/BF02896957
author: Guining Ban
author: ShuXia Yu
published in: Science in China. Series A
publication date: 1998-05-12T00:00:00Z
review text: It is known for odd prime \(p\) that an abelian group of order not more than \(p^7\) can not be the (full) automorphism group of a finite group [see \textit{D. Flannery, D. McHale}, Proc. R. Ir. Acad., Sect. A 81, 209-215 (1981; Zbl 0479.20015)]\ while the order \(p^{12}\) is possible [see \textit{M. Morigi}, Commun. Algebra 23, No. 6, 2045-2065 (1995; Zbl 0836.20019)]. The purpose of this paper is to reduce this gap: It is shown, that no abelian group of order \(p^8\) or \(p^9\) occurs as automorphism group. The proof is by restriction, treating the remaining cases one by one.
Mathematics Subject Classification ID: 20D45
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20F29
Mathematics Subject Classification ID: 20F28
zbMATH DE Number: 1066837
zbMATH Keywords: finite \(p\)-groups
zbMATH Keywords: automorphism groups of groups
reviewed by: Hermann Heineken
MaRDI profile type: Publication
cites work: Q4025606
cites work: Q4320274
cites work: Q4885048
cites work: Q4879937
cites work: On finite groups whose automorphism groups are nilpotent
cites work: Q3936904
cites work: Q3043353
cites work: Some non-abelian p-groups with abelian automorphism groups
cites work: On the minimal number of generators of finite non-abelian p-groups having an abelian automorphism group
cites work: On the Automorphism Group of a Finite p-Group with a Small Central Quotient
cites work: On the Automorphism Group of a Finite p-Group with the Central Quotient Metacyclic
cites work: On p-groups with odd order automorphism groups
cites work: Q4200361
cites work: LA-groups
description: scientific article; zbMATH DE number 1066837