(2,m,n)-groups with Euler characteristic equal to -2^as^b

TL;DR

This paper classifies certain almost simple (2,m,n)-groups with Euler characteristic as a product of two prime powers, focusing on those not isomorphic to PSL_2(q) or PGL_2(q).

Contribution

It provides a complete classification of (2,m,n)-groups with specific Euler characteristic properties, excluding well-known isomorphic cases.

Findings

Classified all such (2,m,n)-groups not isomorphic to PSL_2(q) or PGL_2(q).

Identified conditions under which the Euler characteristic is a product of two prime powers.

Enhanced understanding of the structure of almost simple (2,m,n)-groups.

Abstract

We study those $(2,m,n)$-groups which are almost simple and for which the absolute value of the Euler characteristic is a product of two prime powers. All such groups which are not isomorphic to $PSL_2(q)$ or $PGL_2(q)$ are completely classified.