Group extensions and cohomology groups
type: Item
instance of: scholarly article
title: Group extensions and cohomology groups
zbMATH Open document ID: 0723.20030
published in: Journal of Algebra
publication date: 1993-01-01T00:00:00Z
review text: Let \(q\geq 2\) be an integer and let G be a finite group which is assumed to have odd order if \(q\geq 3\). We show that there is a finite group extension \(\tilde G\) of G with abelian kernel such that the inflation map inf: \(H^ q(G,{\mathbb{Q}}/Z)\to H^ q(\tilde G,{\mathbb{Q}}/Z)\) is trivial. For \(q=2\) our construction yields a representation group \(\tilde G\) for G in the sense of I. Schur. The proof makes use of basic results of algebraic number theory and class field theory.
Mathematics Subject Classification ID: 20J06
Mathematics Subject Classification ID: 20E22
Mathematics Subject Classification ID: 11R34
zbMATH DE Number: 4192002
zbMATH Keywords: finite group
zbMATH Keywords: finite group extension
zbMATH Keywords: inflation map
zbMATH Keywords: representation group
author: Hans Opolka
reviewed by: Hans Opolka
MaRDI profile type: Publication
full work available at URL: jabr.1993.1068
OpenAlex ID: W2002407734
DOI: 10.1006/JABR.1993.1068
description: scientific article; zbMATH DE number 4192002