Finite simple exceptional groups of Lie type in which all the subgroups of odd index are pronormal

Abstract

A subgroup $H$ of a group $G$ is said to be pronormal in $G$ if $H$ and $H^g$ are conjugate in $⟨H,H^g⟩$ for every $g\in G$. In this paper we classify finite simple groups $E_6(q)$ and ${}^2{E}_6(q)$ in which all the subgroups of odd index are pronormal. Thus, we complete a classification of finite simple exceptional groups of Lie type in which all the subgroups of odd index are pronormal.

15 pages

References in corpus (1)

• Pronormality of Hall subgroups in finite simple groups