Toroidal Embeddings of Right Groups

TL;DR

This paper investigates how Cayley graphs of right groups can be embedded on surfaces, specifically characterizing those with toroidal embeddings but no planar embeddings, under certain generating system conditions.

Contribution

It provides a characterization of right groups whose Cayley graphs are toroidally embeddable but not planar, with a focus on minimal generating systems.

Findings

Identifies conditions for toroidal embeddings of Cayley graphs of right groups.

Characterizes right groups with non-planar but toroidal Cayley graph embeddings.

Links group generating systems to surface embedding properties.

Abstract

In this note we study embeddings of Cayley graphs of right groups on surfaces. We characterize those right groups which have a toroidal but no planar Cayley graph, such that the generating system of the right group has a minimal generating system of the group as a factor.