Coverings of Groups, Regular Dessins, and Surfaces
Combinatorics
2024-09-04 v1
Abstract
A coset geometry representation of regular dessins is established, and employed to describe quotients and coverings of regular dessins and surfaces. A characterization is then given of face-quasiprimitive regular dessins as coverings of unicellular regular dessins. It shows that there are exactly three O'Nan-Scott-Praeger types of face-quasiprimitive regular dessins which are smooth coverings of unicellular regular dessins, leading to new constructions of interesting families of regular dessins. Finally, a problem of determining smooth Schur covering of simple groups is initiated by studying coverings between and , giving rise to interesting regular dessins like Fibonacci coverings.
Cite
@article{arxiv.2409.01979,
title = {Coverings of Groups, Regular Dessins, and Surfaces},
author = {Jiyong Chen and Wenwen Fan and Cai Heng Li and Yan Zhou Zhu},
journal= {arXiv preprint arXiv:2409.01979},
year = {2024}
}