Symmetry of surfaces for linear fractional group

TL;DR

This paper computes the stable upper genus for a specific family of finite simple groups, linking algebraic group theory with geometric and topological classifications.

Contribution

It provides the first detailed calculation of the stable upper genus for PSL_2(F_p) groups where p ≡ 3 mod 4, bridging group theory with geometric topology.

Findings

Determined the stable upper genus for PSL_2(F_p) with p ≡ 3 mod 4

Connected group theoretical properties with geometric classifications

Enhanced understanding of the interplay between algebra and topology in surface symmetries.

Abstract

We will compute the stable upper genus for the family of finite non-abelian simple groups $PSL_2(\mathbb{F}_p)$ for $p \equiv 3~(mod~4)$. This classification is well-grounded in the other branches of Mathematics like topology, smooth, and conformal geometry, algebraic categories.