Coleman automorphisms of holomorphs of finite abelian groups.
type: Item
instance of: scholarly article
title: Coleman automorphisms of holomorphs of finite abelian groups.
zbMATH Open document ID: 1307.16032
author: Zhengxing Li
author: Jinke Hai
publication date: 2014-09-11T00:00:00Z
review text: Let \(G\) be a finite group, \(\mathbb ZG\) its integral group ring. The authors, in a series of papers, a recent one is [J. Algebra Appl. 13, No. 5, Article ID 1350156 (2014; Zbl 1303.16038)], consider the normalizer problem, that is, whether in \(U\mathbb ZG)\) the normalizer \(N_{U(\mathbb ZG)}(G)\) is \(GZ(U(\mathbb ZG))\), and also the group \(\text{Out}_C(G)\) of outer Coleman automorphisms of \(G\), because triviality of \(\text{Out}_C(G)\) implies the normalizer property for \(G\). The main result of the paper is that if \(H\) is the holomorph of a finite abelian group then \(\text{Out}_C(H)\) is trivial.
reviewed by: János Kurdics
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20D45
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 6342520
zbMATH Keywords: Coleman automorphisms
zbMATH Keywords: integral group rings
zbMATH Keywords: normalizer property
zbMATH Keywords: finite Abelian groups
zbMATH Keywords: holomorphs
MaRDI profile type: Publication
full work available at URL: s10114-014-2143-6
OpenAlex ID: W1999809727
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DOI: 10.1007/S10114-014-2143-6
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published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 6342520