Faithful irreducible representations of metacyclic groups
type: Item
instance of: scholarly article
title: Faithful irreducible representations of metacyclic groups
zbMATH Open document ID: 0820.20009
author: Hyo-Seob Sim
published in: Journal of Algebra
publication date: 1995-09-11T00:00:00Z
review text: The author proves some results on the representations of metacyclic groups. One of these is the following: A metacyclic group has a faithful irreducible representation over a field \(\mathbb{F}\) is and only if the center of the group is cyclic and the characteristic of \(\mathbb{F}\) does not divide the order of the Fitting group. As an application of these results, it is shown that, for an odd prime \(p\), over the field of complex numbers, there are exactly \(p - 1\) linear isomorphic types of linear groups abstractly isomorphic to some metacyclic group of order \(p^ 6\). The author seems unaware of the fact that there are related results in the literature.
reviewed by: B.G.Basmaji
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20C05
zbMATH DE Number: 705009
zbMATH Keywords: cyclic center
zbMATH Keywords: representations of metacyclic groups
zbMATH Keywords: faithful irreducible representations
zbMATH Keywords: Fitting groups
zbMATH Keywords: linear groups
MaRDI profile type: Publication
full work available at URL: jabr.1994.1369
OpenAlex ID: W2088590086
DOI: 10.1006/JABR.1994.1369
description: scientific article; zbMATH DE number 705009