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Bases for quasisimple linear groups

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Title: Bases for quasisimple linear groups
Authors: Lee, M
Liebeck, MW
Item Type: Journal Article
Abstract: 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 stabiliser in G is trivial. We prove that if G is a quasisimple group (i.e. Gis 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 orm−2, and classical groups with natural module of dimension d over subfields of Fq.
Issue Date: 6-Oct-2018
Date of Acceptance: 6-Jun-2018
URI: http://hdl.handle.net/10044/1/61153
DOI: https://doi.org/10.2140/ant.2018.12.1537
ISSN: 1937-0652
Publisher: Mathematical Sciences Publishers
Start Page: 1537
End Page: 1557
Journal / Book Title: Algebra and Number Theory
Volume: 12
Issue: 6
Copyright Statement: © 2018 Mathematical Sciences Publishers.
Keywords: Science & Technology
Physical Sciences
Mathematics
linear groups
simple groups
representations
primitive permutation groups
bases of permutation groups
FINITE CLASSICAL-GROUPS
FIXED-POINT RATIOS
PROJECTIVE-REPRESENTATIONS
MINIMAL DEGREES
REGULAR ORBITS
SIZES
General Mathematics
0101 Pure Mathematics
Publication Status: Published
Online Publication Date: 2018-10-06
Appears in Collections:Pure Mathematics
Faculty of Natural Sciences
Mathematics