Vol. 12, No. 6, 2018

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 10, 1681–1865
Issue 9, 1533–1680
Issue 8, 1359–1532
Issue 7, 1239–1357
Issue 6, 1127–1237
Issue 5, 981–1126
Issue 4, 805–980
Issue 3, 541–804
Issue 2, 267–539
Issue 1, 1–266

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Bases for quasisimple linear groups

Melissa Lee and Martin W. Liebeck

Vol. 12 (2018), No. 6, 1537–1557

Let V be a vector space of dimension d over Fq, a finite field of q elements, and let G GL(V )GLd(q) be a linear group. A base for G is a set of vectors whose pointwise stabilizer in G is trivial. We prove that if G is a quasisimple group (i.e., G is perfect and GZ(G) is simple) acting irreducibly on V , then excluding two natural families, G has a base of size at most 6. The two families consist of alternating groups Altm acting on the natural module of dimension d = m 1 or m 2, and classical groups with natural module of dimension d over subfields of Fq.

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

linear groups, simple groups, representations, primitive permutation groups, bases of permutation groups
Mathematical Subject Classification 2010
Primary: 20C33
Secondary: 20B15, 20D06
Received: 20 February 2018
Revised: 10 April 2018
Accepted: 6 June 2018
Published: 6 October 2018
Melissa Lee
Department of Mathematics
Imperial College
United Kingdom
Martin W. Liebeck
Department of Mathematics
Imperial College
United Kingdom