Fixed point ratios in actions of finite classical groups, III
Fixed point ratios in actions of finite classical groups, III
复制标题
有限经典群作用中的不动点比率，III
DOI：
10.1016/j.jalgebra.2006.05.024
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发表时间：
2007
影响因子：
0.9
通讯作者：
Timothy C. Burness
中科院分区：
文献类型：
--
作者：
Timothy C. Burness
本文是关于有限经典群非子空间作用下不动点比的四篇系列论文中的第二篇。我们的主要结果表明，如果G是一个有限的几乎简单经典群，Ω是一个忠实的传递非子空间G集，那么对于所有素数阶的元素x∈G，或者（G，Ω）是少数已知例外之一。本文记录了一些初步结果，并证明了稳定子g ω包含在Aschbacher族Ci中的一个极大非子空间子群中的主要定理，其中Ci为4≤i≤8。
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 Ω is a faithful transitive non-subspace G-set then either [Formula: see text] for all elements x∈G of prime order, or (G,Ω) 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 Gωis contained in a maximal non-subspace subgroup which lies in one of the Aschbacher families Ci, where 4⩽i⩽8.