Automorphism groups of cyclic p-gonal pseudo-real Riemann surfaces

In this article we prove that the full automorphism group of a cyclic p-gonal pseudo-real Riemann surface of genus g   is either a semidirect product Cn⋉CpCn⋉Cp or a cyclic group, where p   is a prime >2 and g>(p−1)2g>(p−1)2. We obtain necessary and sufficient conditions for the existence of a cyclic p-gonal pseudo-real Riemann surface with full automorphism group isomorphic to a given finite group. Finally we describe some families of cyclic p-gonal pseudo-real Riemann surfaces where the order of the full automorphism group is maximal and show that such families determine real 2-manifolds embedded in the branch locus of moduli space.