Structure of finite, minimal nonabelian groups and triangularization.
type: Item
instance of: scholarly article
title: Structure of finite, minimal nonabelian groups and triangularization.
zbMATH Open document ID: 1175.20007
author: Mitja Mastnak
author: H. Radjavi
published in: Linear Algebra and its Applications
publication date: 2009-03-17T00:00:00Z
review text: Using classical results of \textit{G. A. Miller} and \textit{H. C. Moreno} [Trans. Am. Math. Soc. 4, 398-404 (1903; JFM 34.0173.01)], the irreducible representations of finite, minimal non-Abelian groups are explicitly described and further results about these groups are derived. These are used to provide new answers to questions of the following form: If \(f\) is a homogeneous polynomial in two non-commuting variables, what conditions can be imposed so that whenever, for all \(A\), \(B\) in a semigroup of complex matrices (or compact operators on a Banach space), \(f(A,B)\) is ``small'' in some sense (e.g. is zero, nilpotent, quasi-nilpotent etc.), then the semigroup is triangularizable, or at least reducible?
reviewed by: Hans Lausch
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 20M20
zbMATH DE Number: 5529490
zbMATH Keywords: irreducible representations
zbMATH Keywords: minimal non-Abelian groups
zbMATH Keywords: semigroups of matrices
zbMATH Keywords: triangularizability
zbMATH Keywords: reducibility
MaRDI profile type: Publication
full work available at URL: j.laa.2008.09.018
OpenAlex ID: W2092543316
cites work: Approximate permutability of traces on semigroups of matrices
cites work: How small can nonzero commutators be?
cites work: Q4126536
cites work: Q5708191
DOI: 10.1016/J.LAA.2008.09.018
description: scientific article; zbMATH DE number 5529490