1. Coverings of Groups, Regular Dessins, and Surfaces
- Author
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Chen, Jiyong, Fan, Wenwen, Li, Cai Heng, and Zhu, Yan Zhou
- Subjects
Mathematics - Combinatorics ,20B15, 20B30, 05C25 - 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.
- Published
- 2024