On maximal embeddings of finite quasisimple groups

TL;DR

This paper investigates conditions under which finite quasisimple groups embed maximally into classical groups, identifying specific exceptions related to Ree and sporadic groups.

Contribution

It characterizes maximal embeddings of finite quasisimple groups into classical groups, highlighting particular exceptions involving Ree and sporadic groups.

Findings

Normalizers of embedded groups are maximal subgroups in most cases.

Identifies specific exceptions involving Ree and sporadic simple groups.

Provides criteria based on minimal degrees of projective representations.

Abstract

If a finite quasisimple group G with simple quotient S is embedded into a suitable classical group X through the smallest degree of a projective representation of S, then the normalizer of G in X is a maximal subgroup of X, up to two series of exceptions where S is a Ree group, and four exceptions where S is sporadic.