Projective representations, abelian \(F\)-groups, and central extensions
type: Item
instance of: scholarly article
title: Projective representations, abelian \(F\)-groups, and central extensions
zbMATH Open document ID: 0791.20007
author: Eunmi C. Hwang
published in: Journal of Algebra
publication date: 1994-06-14T00:00:00Z
review text: Let \(F^*\) be the multiplicative group of a field \(F\), let \(G\) be a finite group and let \(\alpha \in Z^ 2(G,F^*)\). Denote by \(F^ \alpha G\) the corresponding twisted group algebra. The main result of the paper is the following Theorem: Finding a group \(G\) with a noncobounding 2- cocycle \(\alpha\) of finite order such that all \(F\)-classes of \(G\) are \(D_ \Gamma\)-regular for \(\Gamma= F^ \alpha G\) is equivalent to finding a group \(H\) with \(p'\)-cyclic subgroup \(A\) such that a primitive \(| A|\)-th root of unity is contained in \(F\), \(1 \neq A \subseteq Z(H) \cap H'(F)\), and such that \(A\) contains no \(F\)-commutator elements of \(H\) except the identity (here \(H'(F)\) is the group generated by all \(F\)-commutators in \(H\)).
reviewed by: G.Karpilovsky
Mathematics Subject Classification ID: 20C25
Mathematics Subject Classification ID: 16S35
zbMATH DE Number: 436489
zbMATH Keywords: finite group
zbMATH Keywords: twisted group algebra
zbMATH Keywords: noncobounding 2-cocycle
MaRDI profile type: Publication
full work available at URL: jabr.1993.1186
OpenAlex ID: W2093348828
DOI: 10.1006/JABR.1993.1186
description: scientific article; zbMATH DE number 436489