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Fixed point ratios in actions of finite classical groups, I

Fixed point ratios in actions of finite classical groups, I
Fixed point ratios in actions of finite classical groups, I
This is the first in a series of four papers on fixed point ratios in 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. Here fpr(x) denotes the proportion of points in ? which are fixed by x. In this introductory note we present our results and describe an application to the study of minimal bases for primitive permutation groups. A further application concerning monodromy groups of covers of Riemann surfaces is also outlined.
finite classical group, fixed point ratio, primitive permutation group
0021-8693
69-79
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, I. Journal of Algebra, 309 (1), 69-79. (doi:10.1016/j.jalgebra.2006.05.024).

Record type: Article

Abstract

This is the first in a series of four papers on fixed point ratios in 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. Here fpr(x) denotes the proportion of points in ? which are fixed by x. In this introductory note we present our results and describe an application to the study of minimal bases for primitive permutation groups. A further application concerning monodromy groups of covers of Riemann surfaces is also outlined.

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

Identifiers

Local EPrints ID: 46630
URI: http://eprints.soton.ac.uk/id/eprint/46630
DOI: doi:10.1016/j.jalgebra.2006.05.024
ISSN: 0021-8693
PURE UUID: 242ca41d-2840-4125-b652-fe08749944d2

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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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