On finite groups all of whose elements of the same order are conjugate in their automorphism groups
type: Item
instance of: scholarly article
title: On finite groups all of whose elements of the same order are conjugate in their automorphism groups
zbMATH Open document ID: 0767.20009
DOI: 10.1016/0021-8693(92)90146-D
published in: Journal of Algebra
publication date: 1993-03-28T00:00:00Z
review text: The aim of the paper under review is to study finite AT-groups (defined in the title). The main result is Theorem 3.1 that describes the general structure of arbitrary AT-groups using the classification of finite simple groups. Its statement is too long, we can mention only that a simple AT-group is isomorphic to either \(L_ 3(4)\), or \(L_ 2(q)\) for suitable \(q\in\{5,7,8,9\}\). The author considers also solvable AT-groups. In particular, it is proved that the Suzuki groups \(A(n,\theta)\) and the Sylow 2-subgroups of \(U_ 3(2^ n)\) are AT-groups. However, the question whether other Suzuki groups are AT-groups remains open.
reviewed by: S. A. Syskin
Mathematics Subject Classification ID: 20D45
Mathematics Subject Classification ID: 20D05
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 130478
zbMATH Keywords: finite \(AT\)-groups
zbMATH Keywords: classification of finite simple groups
zbMATH Keywords: simple \(AT\)- group
zbMATH Keywords: solvable \(AT\)-groups
zbMATH Keywords: Suzuki groups
zbMATH Keywords: Sylow 2-subgroups
author: Jiping Zhang
MaRDI profile type: Publication
cites work: Involutions in Chevalley groups over fields of even order
cites work: Maximal subgroups and automorphisms of Chevalley groups
cites work: Q5662096
cites work: Q5668957
cites work: Q3684278
cites work: Character Table and Blocks of Finite Simple Triality Groups 3 D 4 (q)
cites work: On finite rational groups and related topics
cites work: Groups with an automorphism group which is transitive on the elements of prime order
cites work: Q5577154
cites work: On finite simple groups of characteristic 2 type
cites work: 2-automorphic 2-groups
cites work: Transitive linear groups and linear groups which contain irreducible subgroups of prime order
cites work: Q3934684
cites work: On finite automorphic algebras
cites work: On the triviality of finite automorphic algebras
cites work: Q3712472
cites work: Influence ofS-quasinormality condition on almost minimal subgroups of a finite group
cites work: Q4946884
description: scientific article; zbMATH DE number 130478