Class-preserving Coleman automorphisms of finite groups
type: Item
instance of: scholarly article
title: Class-preserving Coleman automorphisms of finite groups
zbMATH Open document ID: 1004.20011
author: Martin Hertweck
published in: Monatshefte für Mathematik
publication date: 2002-09-10T00:00:00Z
review text: Let \(G\) be a finite group with dihedral or generalized quaternion Sylow 2-subgroup. Let \(A\) be the group of automorphisms of \(G\) which preserve conjugacy classes of \(G\) and whose restriction to any Sylow subgroup is given by conjugation with an element in \(G\). The author shows that then the quotient of \(A\) by the group of inner automorphisms of \(G\) is of odd order. The interest in this type of questions mainly comes from the author's recent spectacular counterexample to the isomorphism problem for integral group rings. There, this class of automorphisms is intensively used. The proof of the present paper also is a followup of the author's sophisticated technique which he developed for his example.
reviewed by: Alexander Zimmermann
Mathematics Subject Classification ID: 20D45
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20E45
zbMATH DE Number: 1798922
zbMATH Keywords: class preserving automorphisms
zbMATH Keywords: finite groups
zbMATH Keywords: groups of automorphisms
zbMATH Keywords: conjugacy classes
zbMATH Keywords: Sylow subgroups
zbMATH Keywords: groups of inner automorphisms
zbMATH Keywords: isomorphism problem for integral group rings
MaRDI profile type: Publication
full work available at URL: s006050200029
OpenAlex ID: W1983320580
DOI: 10.1007/S006050200029
description: scientific article; zbMATH DE number 1798922