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Fixed point ratios in actions of finite classical groups, II

By Timothy C. Burness

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

Topics: QA
Year: 2007
OAI identifier: oai:eprints.soton.ac.uk:46631
Provided by: e-Prints Soton
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