Semisymmetric cubic graphs of twice odd order

The groups which can act semisymmetrically on a cubic graph of twice odd order are determined modulo a normal subgroup which acts semiregularly on the vertices of the graph

The commuting graph of a soluble group

The commuting graph of a finite soluble group with trivial centre is investigated. It is shown that the diameter of such a graph is at most 8 or the graph is disconnected. Examples of soluble groups with trivial centre and commuting graph of diameter 8 are provided

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

There is no upper bound for the diameter of the commuting graph of a finite group

We construct a family of finite special 2-groups which have commuting graph of increasing diamete

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