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Fixed point ratios in actions of finite classical groups, III

Fixed point ratios in actions of finite classical groups, III
Fixed point ratios in actions of finite classical groups, III
This is the third in a series of four papers on fixed point ratios for 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 consider the case where G? is contained in one of the Aschbacher families ?2 or ?3.
finite classical group, fixed point ratio, primitive permutation group
0021-8693
693-748
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, III. Journal of Algebra, 314 (2), 693-748. (doi:10.1016/j.jalgebra.2007.01.011).

Record type: Article

Abstract

This is the third in a series of four papers on fixed point ratios for 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 consider the case where G? is contained in one of the Aschbacher families ?2 or ?3.

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Published date: 15 August 2007
Keywords: finite classical group, fixed point ratio, primitive permutation group

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Local EPrints ID: 46632
URI: http://eprints.soton.ac.uk/id/eprint/46632
ISSN: 0021-8693
PURE UUID: 399a2fc3-9d26-4b28-be68-e4ca8ae569ba

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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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