Embedding central extensions of simple linear groups into wreath products

TL;DR

This paper establishes a criterion for embedding certain central extensions of simple linear groups into wreath products, specifically focusing on extensions of PSL_n(q) with prime order kernels and their permutation actions.

Contribution

It provides a new criterion for embedding nonsplit central extensions of PSL_n(q) into permutation wreath products based on their action on projective space.

Findings

Derived a criterion for embedding central extensions into wreath products

Applied the criterion to extensions of PSL_n(q) with prime order kernels

Enhanced understanding of the structure of linear groups and their extensions

Abstract

We find a criterion for the embedding of a nonsplit central extension of $PSL_n(q)$ with kernel of prime order into the permutation wreath product that corresponds to the action on the projective space.