Burness, Timothy C.
(2007)
Fixed point ratios in actions of finite classical groups, II.
*Journal of Algebra*, 309 (1), 80-138.
(doi:10.1016/j.jalgebra.2006.05.025).

## 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.

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