Finite simple groups acting with fixity 4 and their occurrence as groups of automorphisms of Riemann surfaces (extended version)

TL;DR

This paper classifies finite simple groups that act on Riemann surfaces with fixity 4, identifying which can act faithfully with this property on surfaces of genus at least 2, and includes computational code for verification.

Contribution

It extends previous classifications by determining which finite simple groups can act with fixity 4 on Riemann surfaces of genus at least 2, providing explicit computational tools.

Findings

Identified specific finite simple groups capable of such actions

Provided GAP code for verifying group actions

Extended classification of group actions on Riemann surfaces

Abstract

In previous work, all finite simple groups that act with fixity 4 have been classified. In this article we investigate which ones of these groups act faithfully on a compact Riemann surface of genus at least 2 with fixity four in total and in such a way that fixity 4 is exhibited on at least one orbit. This is an extended version of the submitted article, including our GAP code.