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arXiv · 2409.01979

Coverings of Groups, Regular Dessins, and Surfaces

Jiyong Chen·Wenwen Fan·Cai Heng Li·Yan Zhou Zhu
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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 $\SL(2,p)$ and $\PSL(2,p)$, giving rise to interesting regular dessins like Fibonacci coverings.

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Jiyong Chen, Wenwen Fan, Cai Heng Li, Yan Zhou Zhu. 2024-09-03. Coverings of Groups, Regular Dessins, and Surfaces. https://arxiv.org/abs/2409.01979

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