Generalized quasi-dihedral group as automorphism group of Riemann surfaces

TL;DR

This paper investigates the actions of generalized quasi-dihedral groups on various types of Riemann and Klein surfaces, focusing on conformal and anticonformal symmetries and their uniqueness up to homeomorphism.

Contribution

It characterizes the actions of generalized quasi-dihedral groups on Riemann and Klein surfaces and examines their uniqueness, extending understanding of automorphism groups in complex analysis.

Findings

Identifies conditions for conformal and anticonformal actions of G_n

Establishes uniqueness (up to homeomorphism) of these actions

Provides classifications for pseudo-real and Klein surfaces with such symmetries

Abstract

In this paper, we discuss certain types of conformal/anticonformal actions of the generalized quasi-dihedral group $G_{n}$ of order $8n$, for $n\geq 2$, on closed Riemann surfaces, pseudo-real Riemann surfaces and compact Klein surfaces, and in each of these actions we study the uniqueness (up to homeomorphisms) action problem.