On the characters of the group of upper-triangular matrices
type: Item
instance of: scholarly article
title: On the characters of the group of upper-triangular matrices
zbMATH Open document ID: 0863.20006
author: Balázs Szegedy
published in: Journal of Algebra
publication date: 1997-06-03T00:00:00Z
review text: The author shows that all complex characters of certain finite groups are monomial (groups with this property are called \(M\)-groups). The groups under consideration are defined as the groups of units of certain finite associative algebras. Let \(K\) be a finite field of \(q\) elements, and \(A\) a finite (dimensional) algebra over \(K\). Then \(A\) is called a \(DN\)-algebra if \(A/\text{Rad }A\) is a direct sum of copies of \(K\). The author proves that the group \(G(A)\) of units of \(A\) is an \(M\)-group, and that the degrees of complex characters of \(G(A)\) are of shape \(q^r(q-1)^s\) for some integers \(r,s\geq 0\).
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 16P10
Mathematics Subject Classification ID: 16G30
Mathematics Subject Classification ID: 16U60
zbMATH DE Number: 954745
zbMATH Keywords: complex characters
zbMATH Keywords: finite groups
zbMATH Keywords: \(M\)-groups
zbMATH Keywords: groups of units
zbMATH Keywords: finite associative algebras
zbMATH Keywords: finite fields
zbMATH Keywords: \(DN\)-algebras
MaRDI profile type: Publication
full work available at URL: jabr.1996.0365
OpenAlex ID: W2019337178
DOI: 10.1006/JABR.1996.0365
description: scientific article; zbMATH DE number 954745