#### Vol. 12, No. 6, 2018

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions 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
Bases for quasisimple linear groups

### Melissa Lee and Martin W. Liebeck

Vol. 12 (2018), No. 6, 1537–1557
##### Abstract

Let $V$ be a vector space of dimension $d$ over ${\mathbb{F}}_{q}$, a finite field of $q$ elements, and let $G\le GL\left(V\right)\cong {GL}_{d}\left(q\right)$ 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 $G∕Z\left(G\right)$ 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 ${Alt}_{m}$ 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 ${\mathbb{F}}_{q}$.

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/ant

We have not been able to recognize your IP address 52.23.219.12 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

or by using our contact form.