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Fixed point ratios in actions of finite classical groups, II

Fixed point ratios in actions of finite classical groups, II
Fixed point ratios in actions of finite classical groups, II
This is the second in a series of four papers on fixed point ratios in non-subspace actions of finite classical groups. Our main result states that if G is a finite almost simple classical group and ? is a faithful transitive non-subspace G-set then either fpr(x) ~< |xG|-1/2 for all elements x?G of prime order, or (G,?) is one of a small number of known exceptions. In this paper we record a number of preliminary results and prove the main theorem in the case where the stabiliser G? is contained in a maximal non-subspace subgroup which lies in one of the Aschbacher families ?i, where 4?i?8.
finite classical group, fixed point ratio, primitive permutation group
0021-8693
80-138
Burness, Timothy C.
a3b369f0-16f5-41e6-84d9-5a50f027bcd6
Burness, Timothy C.
a3b369f0-16f5-41e6-84d9-5a50f027bcd6

Burness, Timothy C. (2007) Fixed point ratios in actions of finite classical groups, II. Journal of Algebra, 309 (1), 80-138. (doi:10.1016/j.jalgebra.2006.05.025).

Record type: Article

Abstract

This is the second in a series of four papers on fixed point ratios in non-subspace actions of finite classical groups. Our main result states that if G is a finite almost simple classical group and ? is a faithful transitive non-subspace G-set then either fpr(x) ~< |xG|-1/2 for all elements x?G of prime order, or (G,?) is one of a small number of known exceptions. In this paper we record a number of preliminary results and prove the main theorem in the case where the stabiliser G? is contained in a maximal non-subspace subgroup which lies in one of the Aschbacher families ?i, where 4?i?8.

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Published date: 1 March 2007
Keywords: finite classical group, fixed point ratio, primitive permutation group

Identifiers

Local EPrints ID: 46631
URI: http://eprints.soton.ac.uk/id/eprint/46631
DOI: doi:10.1016/j.jalgebra.2006.05.025
ISSN: 0021-8693
PURE UUID: 81dd82a5-b3f1-41f4-8f98-a8caeeffe059

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Date deposited: 09 Jul 2007
Last modified: 15 Mar 2024 09:25

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Author: Timothy C. Burness

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