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Fixed point ratios in actions of finite classical groups, IV

By Timothy C. Burness


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

Topics: QA
Year: 2007
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Provided by: e-Prints Soton
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