Automorphisms of nonsplit coverings of $PSL_2(q)$ in odd characteristic dividing $q-1$

TL;DR

This paper classifies certain nonsplit group extensions involving PSL_2(q) in odd characteristic, computes their cohomology, and describes their automorphism groups, advancing understanding of their algebraic structure.

Contribution

It provides a detailed classification and automorphism description of nonsplit extensions of elementary abelian p-groups by PSL_2(q) in odd characteristic dividing q-1.

Findings

Classification of nonsplit extensions of elementary abelian p-groups by PSL_2(q)

Calculation of relevant low-dimensional cohomology groups

Description of automorphism groups of these extensions

Abstract

We classify the nonsplit extensions of elementary abelian $p$-groups by $PSL_2(q)$, with odd $p$ dividing $q-1$, for an irreducible induced action, calculate the relevant low-dimensional cohomology groups, and describe the automorphism groups of such extensions.