A classification of regular maps with Euler characteristic $-pq$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866912837034573824 |
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| author | Li, Xiaogang Tian, Yao |
| author_facet | Li, Xiaogang Tian, Yao |
| contents | In this paper, we give a classification of regular maps with Euler characteristic $-pq$ for distinct primes $q>p\geq 5$. This together with previous classification of regular maps with Euler characteristic $-2p,-3p$ and $-p^2$ completes the classification of regular maps with Euler characteristic $-pq$ for two primes $p$ and $q$. An interesting consequence is that, for every pair of twin primes $p$ and $q$ greater than $5$, there exist three regular maps with solvable automorphism groups and Euler characteristic $-pq$, up to duality and isomorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14635 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A classification of regular maps with Euler characteristic $-pq$ Li, Xiaogang Tian, Yao Group Theory Combinatorics 05C10, 20B25 In this paper, we give a classification of regular maps with Euler characteristic $-pq$ for distinct primes $q>p\geq 5$. This together with previous classification of regular maps with Euler characteristic $-2p,-3p$ and $-p^2$ completes the classification of regular maps with Euler characteristic $-pq$ for two primes $p$ and $q$. An interesting consequence is that, for every pair of twin primes $p$ and $q$ greater than $5$, there exist three regular maps with solvable automorphism groups and Euler characteristic $-pq$, up to duality and isomorphism. |
| title | A classification of regular maps with Euler characteristic $-pq$ |
| topic | Group Theory Combinatorics 05C10, 20B25 |
| url | https://arxiv.org/abs/2601.14635 |