On planar right groups

TL;DR

This paper characterizes which finite right groups have planar Cayley graphs, extending Maschke's work on finite groups to a broader class of semigroups and providing a complete classification.

Contribution

It provides the first complete characterization of planar right groups, a class of semigroups close to groups, in terms of their Cayley graphs.

Findings

Complete classification of planar right groups

Extension of Maschke's characterization to semigroups

Identification of conditions for planarity in right groups

Abstract

In 1896 Heinrich Maschke characterized planar finite groups, that is groups which admit a generating system such that the resulting Cayley graph is planar. In our study we consider the question, which finite semigroups have a planar Cayley graph. Right groups are a class of semigroups relatively close to groups. We present a complete characterization of planar right groups.