On strongly pp-embedded subgroups of Lie rank 2

Suppose that $p$ is a prime, $G$ is a finite group and $H$ is a strongly $p$-embedded subgroup in $G$. We consider the possibility that $F^*(H)$ is a simple group of Lie rank 2 defined in characteristic $p$.Comment: 9 page

An improved 3-local characterisation of McL and its automorphism group

This article presents a 3-local characterisation of the sporadic simple group McL and its automorphism group. The theorem is underpinned by a further identification theorem the proof of which is character theoretic. The main theorem is applied in our investigation of groups with a large 3-subgroup. An additional file containing Magma code has been attached to this submission.Comment: Revised following reviewer comment

An identification theorem for the sporadic simple groups F_2 and M(23)

We identify the sporadic groups M(23) and F_2 from the approximate structure of the centralizer of an element of order 3

On Bruck Loops of 2-power Exponent

The goal of this paper is two-fold. First we provide the information needed to study Bol, $A_r$ or Bruck loops by applying group theoretic methods. This information is used in this paper as well as in [BS3] and in [S]. Moreover, we determine the groups associated to Bruck loops of 2-power exponent under the assumption that every nonabelian simple group $S$ is either passive or isomorphic to \PSL_2(q), $q-1 \ge 4$ a $2$-power. In a separate paper it is proven that indeed every nonabelian simple group $S$ is either passive or isomorphic to \PSL_2(q), $q-1 \ge 4$ a $2$-power [S]. The results obtained here are used in [BS3], where we determine the structure of the groups associated to the finite Bruck loops.Comment: 26 page

The Local Structure Theorem, the non-characteristic 2 case

Let $p$ be a prime, $G$ a finite $\mathcal{K}_p$-group, $S$ a Sylow $p$-subgroup of $G$ and $Q$ be a large subgroup of $G$ in $S$. The aim of the Local Structure Theorem is to provide structural information about subgroups $L$ with $S \leq L$, $O_p(L) \not= 1$ and $L \not\leq N_G(Q)$. There is, however, one configuration where no structural information about $L$ can be given using the methods in the proof of the Local Structure Theorem. In this paper we show that for $p=2$ this hypothetical configuration cannot occur. We anticipate that our theorem will be used in the programme to revise the classification of the finite simple groups