The Full Automorphism Group of a Cyclic $p$-gonal Surface

Abstract

If $p$ is prime, a compact Riemann surface $X$ of genus $g\ge 2$ is called cyclic $p$-gonal if it admits a cyclic group of automorphisms $C_p$ of order $p$ such that the quotient space $X/C_p$ has genus 0. If in addition $C_p$ is not normal in the full automorphism $G$, then we call $G$ a non-normal cyclic $p$-gonal group. In the following we classify all non-normal $p$-gonal groups.

18 pages, 5 figures

References in corpus (1)

• Riemann Surfaces of genus g with an automorphism of order p prime and p>g

Cited by in corpus (2)

• Riemann Surfaces of genus g with an automorphism of order p prime and p>g
• Topologically unique maximal elementary Abelian group actions on compact oriented surfaces