Linear representations of binate groups
type: Item
instance of: scholarly article
title: Linear representations of binate groups
zbMATH Open document ID: 0813.20060
DOI: 10.1016/0022-4049(94)90003-5
author: A. J. Berrick
author: Roger C. Alperin
published in: Journal of Pure and Applied Algebra
publication date: 1995-05-30T00:00:00Z
review text: A binate group \(G\) is a group with the property that for each finitely generated, proper subgroup \(H < G\), there is a homomorphism \(\varphi : H \to G\), and an element \(t \in G \setminus H\) such that for all \(h \in H\), one has \(h = [t,\varphi(h)]\). Such a group is perfect and acyclic (i.e. has vanishing integral homology in all positive dimensions). It is first shown using homological arguments that binate groups have no non-trivial finite-dimensional unitary representations, and then, independently, using results about algebraic groups, that in fact they have no non-trivial finite-dimensional linear representations whatsoever.
Mathematics Subject Classification ID: 20J05
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20C15
zbMATH DE Number: 609788
zbMATH Keywords: finitely generated subgroups
zbMATH Keywords: binate groups
zbMATH Keywords: perfect groups
zbMATH Keywords: acyclic groups
zbMATH Keywords: integral homology
zbMATH Keywords: unitary representations
zbMATH Keywords: linear representations
MaRDI profile type: Publication
full work available at URL: 0022-4049(94)90003-5
OpenAlex ID: W2058897551
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Wikidata QID: Q128023627
description: scientific article; zbMATH DE number 609788