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Fixed point ratios in actions of finite classical groups, IV

Fixed point ratios in actions of finite classical groups, IV
Fixed point ratios in actions of finite classical groups, IV
This is the final paper in a series of four 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 assume G? is either an almost simple irreducible subgroup in Aschbacher's ? collection, or a subgroup in a small additional set N which arises when G has socle Sp4(q)? (q even) or P?8+(q). This completes the proof of the main theorem.
finite classical group, fixed point ratio, primitive permutation group
0021-8693
749-788
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, IV. Journal of Algebra, 314 (2), 749-788. (doi:10.1016/j.jalgebra.2007.01.012).

Record type: Article

Abstract

This is the final paper in a series of four 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 assume G? is either an almost simple irreducible subgroup in Aschbacher's ? collection, or a subgroup in a small additional set N which arises when G has socle Sp4(q)? (q even) or P?8+(q). This completes the proof of the main theorem.

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

Identifiers

Local EPrints ID: 46633
URI: http://eprints.soton.ac.uk/id/eprint/46633
ISSN: 0021-8693
PURE UUID: e3ad5972-1e2f-4654-aed1-364b1a60f8af

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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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