Irreducible groups with submultiplicative spectrum
type: Item
instance of: scholarly article
title: Irreducible groups with submultiplicative spectrum
zbMATH Open document ID: 1070.47031
published in: Linear Algebra and its Applications
publication date: 2004-08-06T00:00:00Z
review text: Let \({\mathcal J}_n\) be a finite group of \(n\times n\) matrices. The spectrum \(\sigma\) is submultiplicative on \({\mathcal J}_n\) if \(\sigma(ST)\subseteq\sigma(S)\sigma(T)=\{\lambda\mu:\lambda\in\sigma(S), \mu\in\sigma(T)\}\) for every \(S,T \in {\mathcal J}_n\). The author proves the existence of irreducible groups with submultiplicative spectrum for every even \(n\) which is divisible by 8. Two examples of such groups are constructed. It is shown that every group of \(2\times 2\) and \(4\times 4\) matrices is reducible.
reviewed by: Michael Perelmuter
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 15A30
zbMATH DE Number: 2081758
zbMATH Keywords: matrix groups
zbMATH Keywords: irreducible groups
zbMATH Keywords: submultiplicative spectrum
author: Marjeta Kramar Fijavž
MaRDI profile type: Publication
full work available at URL: j.laa.2003.09.015
OpenAlex ID: W2077608233
cites work: On groups of central type
cites work: Q4024259
cites work: On 2-groups with submultiplicative spectrum
cites work: Simultaneous triangularization
cites work: Q3994730
cites work: Q4126536
DOI: 10.1016/J.LAA.2003.09.015
description: scientific article; zbMATH DE number 2081758