Images of word maps in almost simple groups and quasisimple groups

TL;DR

This paper investigates the verbal images of almost simple and quasisimple groups, extending Lubotzky's results on simple groups to broader classes of groups.

Contribution

It determines the verbal images of certain almost simple and quasisimple groups using Lubotzky's framework.

Findings

Verbal images of specific almost simple groups identified

Verbal images of certain quasisimple groups characterized

Extension of Lubotzky's results to broader group classes

Abstract

It has been shown by Lubotzky in [10] that the set of verbal images of a fixed non-abelian finite simple group G is precisely the set of endomorphism invariant subsets of G. Here we use his result to determine the verbal images of certain almost simple groups and quasisimple groups.