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

TL;DR

This paper provides a refined 3-local characterization of the McL sporadic simple group and its automorphism group, using character theory, with applications to groups containing large 3-subgroups.

Contribution

It introduces an improved 3-local characterization of McL and its automorphism group based on character theoretic methods, enhancing understanding of their structure.

Findings

New 3-local characterization of McL

Identification theorem based on character theory

Application to groups with large 3-subgroups

Abstract

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.