Fixed point ratios in actions of finite exceptional groups of lie type.
Fixed point ratios in actions of finite exceptional groups of lie type.
复制标题
谎言类型的有限异常群的动作中的不动点比率。
DOI：
10.2140/pjm.2002.205.393
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发表时间：
2002
影响因子：
0.6
通讯作者：
G. Seitz
中科院分区：
文献类型：
--
作者：
R. Lawther;M. Liebeck;G. Seitz
设G是有限的李型例外群，作用在集合O上传递。对于G中的x，x的不动点比是O中被x固定的元素的比例。我们得到了这样的不动点比的新的界。当一个点稳定子是抛物型时，我们使用特征理论;在其他情况下，我们使用Lawther，Liebeck & Seitz，2002中关于代数群的类似问题的结果。这些给维界不动点空间的元素例外代数群，我们适用于通过有限群通过弗罗贝纽斯态射。
Let G be a finite exceptional group of Lie type acting transitively on a set O. For x in G, the fixed point ratio of x is the proportion of elements of O which are fixed by x. We obtain new bounds for such fixed point ratios. When a point-stabilizer is parabolic we use character theory; and in other cases, we use results on an analogous problem for algebraic groups in Lawther, Liebeck & Seitz, 2002. These give dimension bounds on fixed point spaces of elements of exceptional algebraic groups, which we apply by passing to finite groups via a Frobenius morphism.