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
749-788
Burness, Timothy C.
a3b369f0-16f5-41e6-84d9-5a50f027bcd6
15 August 2007
Burness, Timothy C.
a3b369f0-16f5-41e6-84d9-5a50f027bcd6
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
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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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