Regular orbits of linear groups
type: Item
instance of: scholarly article
title: Regular orbits of linear groups
zbMATH Open document ID: 0901.20006
author: Martin W. Liebeck
published in: Journal of Algebra
publication date: 1998-09-27T00:00:00Z
review text: The author shows the following well-known theorem: Let \(p\) be a prime with \(p>5^{30}\). Suppose that \(G\) is a \(p'\)-group and \(V\) is a faithful \(\mathbb{F}_pG\)-module such that \(G\) has a quasi-simple normal subgroup \(H\) which is irreducible on \(V\). Then one of the following holds: (i) \(G\) has a regular orbit on the vectors of \(V\); (ii) \(H=A_c\), \(c<p\), and \(V\) is the ``natural'' module for \(H\).
reviewed by: Ye Jiachen
Mathematics Subject Classification ID: 20C33
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20G05
zbMATH DE Number: 941284
zbMATH Keywords: regular orbits
zbMATH Keywords: finite quasi-simple groups
zbMATH Keywords: faithful modules
MaRDI profile type: Publication
full work available at URL: jabr.1996.0303
OpenAlex ID: W2003765710
DOI: 10.1006/JABR.1996.0303
description: scientific article; zbMATH DE number 941284