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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.01979 |
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| _version_ | 1866913490797592576 |
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| author | Chen, Jiyong Fan, Wenwen Li, Cai Heng Zhu, Yan Zhou |
| author_facet | Chen, Jiyong Fan, Wenwen Li, Cai Heng Zhu, Yan Zhou |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01979 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coverings of Groups, Regular Dessins, and Surfaces Chen, Jiyong Fan, Wenwen Li, Cai Heng Zhu, Yan Zhou Combinatorics 20B15, 20B30, 05C25 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. |
| title | Coverings of Groups, Regular Dessins, and Surfaces |
| topic | Combinatorics 20B15, 20B30, 05C25 |
| url | https://arxiv.org/abs/2409.01979 |