Skew-morphisms of regular Cayley maps

Abstract

A Cayley map M is a 2-cell embedding of a Cayley graph in an orientable surface with the same orientation (the induced permutation of generators) at each vertex. The concept of a skew-morphism generalizes several concepts previously studied with respect to regular Cayley maps, and allows for a unified theory of regular Cayley maps and their automorphism groups. Using algebraic properties of skew-morphisms of groups we reprove or extend some previously known results and obtain several new ones.