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Bases for quasisimple linear groups
File | Description | Size | Format | |
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base-simpleaff.pdf | Accepted version | 413.94 kB | Adobe PDF | View/Open |
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 |