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

Shaofei Du, Hao Yu, Wenjuan Luo

Published 2022-10-03Version 1

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.