Automorphisms of nonsplit extensions of 2-groups by $PSL_2(q)$

TL;DR

This paper fully characterizes the automorphism groups of nonsplit extensions of elementary abelian 2-groups by PSL_2(q) for odd q, and applies these findings to the theory of π-submaximal subgroups.

Contribution

It provides a complete description of automorphism groups for these specific nonsplit extensions, advancing understanding in group extension theory.

Findings

Automorphism groups of all such extensions are explicitly described.

Application to the classification of π-submaximal subgroups.

Enhanced understanding of the structure of nonsplit extensions involving PSL_2(q).

Abstract

We complete the description of automorphism groups of all nonsplit extensions of elementary abelian $2$-groups by $PSL_2(q)$, with $q$ odd, for an irreducible induced action. An application of this result to the theory of $\pi$-submaximal subgroups is given.