论文标题
关于简单组的纠纷固定
On the involution fixity of simple groups
论文作者
论文摘要
令$ g $为有限的度量$ n $，让$ {\ rm ifix}（g）$为$ g $的互动固定性，这是互动的最大固定点。在本文中，我们研究了几乎简单的原始群体的互动固定性，他们的socle $ t $是交替的或零星的群体；我们的主要结果将该表格的组与$ {\ rm ifix}（t）\ leqslant n^{4/9} $分类。这是基于Burness和Thomas的早期工作，他们研究了$ t $是一种杰出的谎言类型的情况，它增强了绑定的$ {\ rm ifix}（t）> n^{1/6} $（有规定的例外），这是Liebeck和Shalev在2015年证明的。类似的成果将在sideclical ned中建立。
Let $G$ be a finite permutation group of degree $n$ and let ${\rm ifix}(G)$ be the involution fixity of $G$, which is the maximum number of fixed points of an involution. In this paper we study the involution fixity of almost simple primitive groups whose socle $T$ is an alternating or sporadic group; our main result classifies the groups of this form with ${\rm ifix}(T) \leqslant n^{4/9}$. This builds on earlier work of Burness and Thomas, who studied the case where $T$ is an exceptional group of Lie type, and it strengthens the bound ${\rm ifix}(T) > n^{1/6}$ (with prescribed exceptions), which was proved by Liebeck and Shalev in 2015. A similar result for classical groups will be established in a sequel.
