论文标题
有限的几乎简单组的小索引的最大亚组
Maximal subgroups of small index of finite almost simple groups
论文作者
论文摘要
We prove in this paper that a finite almost simple group $R$ with socle the non-abelian simple group $S$ possesses a conjugacy class of core-free maximal subgroups whose index coincides with the smallest index $\operatorname{l}(S)$ of a maximal group of $S$ or a conjugacy class of core-free maximal subgroups with a fixed index $v_S \leq {\ operatorname {l}（s）^2} $，仅取决于$ s $。我们表明，$ s $的外部自动形态组的子组数量由$ \ log^3 {\ pereratatorName {l}（s）} $和$ \ operatatorName {l}（l}（s）^2 <| s | $。
We prove in this paper that a finite almost simple group $R$ with socle the non-abelian simple group $S$ possesses a conjugacy class of core-free maximal subgroups whose index coincides with the smallest index $\operatorname{l}(S)$ of a maximal group of $S$ or a conjugacy class of core-free maximal subgroups with a fixed index $v_S \leq {\operatorname{l}(S)^2}$, depending only on $S$. We show that the number of subgroups of the outer automorphism group of $S$ is bounded by $\log^3 {\operatorname{l}(S)}$ and $\operatorname{l}(S)^2 < |S|$.
