Groups which are almost groups of Lie type in characteristic p

Abstract

For a prime $p$, a $p$-subgroup of a finite group $G$ is said to be large if and only if $Q=F^{\ast }(N_G(Q))$ and, for all $1\ne U\le Z(Q)$, $N_G(U)\le N_G(Q)$. In this article we determine those groups $G$ which have a large subgroup and which in addition have a proper subgroup $H$ containing a Sylow $p$-subgroup of $G$ with $F^{\ast }(H)$ a group of Lie type in characteristic $p$ and rank at least 2 (excluding $\PSL_3(p^a)$) and $C_H(z)$ soluble for some $z\in Z(S)$. This work is part of a project to determine the groups $G$ which contain a large $p$-subgroup.

References in corpus (2)

• $F_4(2)$ and its automorphism group
• A characterisation of almost simple groups with socle ${}^2\E_6(2)$ or $\M(22)$

Cited by in corpus (3)

• $F_4(2)$ and its automorphism group
• An identification theorem for the sporadic simple groups F_2 and M(23)
• An improved 3-local characterisation of McL and its automorphism group