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Fixed point ratios in actions of finite exceptional groups of lie type.

Lawther, Ross and Liebeck, Martin W. and Seitz, Gary M. (2002) Fixed point ratios in actions of finite exceptional groups of lie type. Pacific Journal of Mathematics, 205 (2). pp. 393-464. ISSN 0030-8730

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Abstract

Let G be a finite exceptional group of Lie type acting transitively on a set Ø. For x in G, the fixed point ratio of x is the proportion of elements of Ø which are fixed by x. We obtain new bounds for such fixed point ratios. When a point-stabilizer is parabolic we use character theory; and in other cases, we use results on an analogous problem for algebraic groups in Lawther, Liebeck & Seitz, 2002. These give dimension bounds on fixed point spaces of elements of exceptional algebraic groups, which we apply by passing to finite groups via a Frobenius morphism.

Item Type: Article
Journal or Publication Title: Pacific Journal of Mathematics
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 19279
Deposited By: ep_ss_importer
Deposited On: 19 Nov 2008 16:58
Refereed?: Yes
Published?: Published
Last Modified: 09 Apr 2014 20:23
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/19279

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