Finite groups with its power automorphism groups having small indices.
type: Item
instance of: scholarly article
title: Finite groups with its power automorphism groups having small indices.
zbMATH Open document ID: 1184.20022
author: Junxin Wang
author: Xiuyun Guo
publication date: 2009-09-03T00:00:00Z
review text: The paper studies those finite groups \(G\) for which \(|\Aut(G):P(G)|\) is small, where \(P(G)\) is the group of power automorphisms of \(G\). It is shown that \(|\Aut(G):P(G)|\) cannot be a prime. Also, \(|\Aut(G):P(G)|\) is the product of two distinct primes precisely when \(G\) is the direct product of a cyclic group \(A\) with a group \(B\) of coprime order and very restricted (and completely determined) structure.
Mathematics Subject Classification ID: 20D45
Mathematics Subject Classification ID: 20E34
Mathematics Subject Classification ID: 20F28
zbMATH DE Number: 5601606
zbMATH Keywords: finite groups
zbMATH Keywords: power automorphism groups
zbMATH Keywords: norm
zbMATH Keywords: actions
reviewed by: Marian Deaconescu
MaRDI profile type: Publication
full work available at URL: s10114-009-8060-4
OpenAlex ID: W2039605301
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DOI: 10.1007/S10114-009-8060-4
published in: Acta Mathematica Sinica, English Series
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description: scientific article; zbMATH DE number 5601606