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2018 Bases for quasisimple linear groups
Melissa Lee, Martin W. Liebeck
Algebra Number Theory 12(6): 1537-1557 (2018). DOI: 10.2140/ant.2018.12.1537


Let V be a vector space of dimension d over F q , a finite field of q elements, and let G GL ( V ) GL d ( 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 G Z ( 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 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 F q .


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Melissa Lee. Martin W. Liebeck. "Bases for quasisimple linear groups." Algebra Number Theory 12 (6) 1537 - 1557, 2018.


Received: 20 February 2018; Revised: 10 April 2018; Accepted: 6 June 2018; Published: 2018
First available in Project Euclid: 25 October 2018

zbMATH: 06973919
MathSciNet: MR3864206
Digital Object Identifier: 10.2140/ant.2018.12.1537

Primary: 20C33
Secondary: 20B15 , 20D06

Keywords: bases of permutation groups , linear groups , primitive permutation groups , representations , simple groups

Rights: Copyright © 2018 Mathematical Sciences Publishers


Vol.12 • No. 6 • 2018
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