Regular Cayley Maps of Elementary abelian $p$-groups: Classification and Enumeration

TL;DR

This paper provides a complete classification and enumeration of regular Cayley maps on elementary abelian p-groups, expanding understanding of their structure and properties.

Contribution

It offers the first comprehensive classification and enumeration of regular Cayley maps on elementary abelian p-groups, including their genera.

Findings

Complete classification of regular Cayley maps of Z_p^n

Enumeration of the number of such maps

Analysis of their genera

Abstract

Recently, regular Cayley maps of cyclic groups and dihedral groups have been classified. A nature question is to classify regular Cayley maps of elementary abelian $p$-groups $Z_p^n$. In this paper, a complete classification of regular Cayley maps of $Z_p^n$ is given and moreover, the number of these maps and their genera are enumerated.