Maximal subgroups of small index of finite almost simple groups

Abstract

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 $l(S)$ of a maximal group of $S$ or a conjugacy class of core-free maximal subgroups with a fixed index $v_S\le l(S{)}^2$, depending only on $S$. We show that the number of subgroups of the outer automorphism group of $S$ is bounded by ${\log }^{3}l(S)$ and $l(S{)}^2<|S|$.

20 pages There is a change in the title with respect to the first draft. This paper has been published under an open access license thanks to the CRUE-CSIC agreement with Springer Nature