A classification of vertex-reversing maps with Euler characteristic coprime to the edge number
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909963986665472 |
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| author | Li, Cai Heng Liu, Luyi Yi, Hanyue |
| author_facet | Li, Cai Heng Liu, Luyi Yi, Hanyue |
| contents | A map is \emph{vertex-reversing} if it admits an arc-transitive automorphism group with dihedral vertex stabilizers. This paper classifies solvable vertex-reversing maps whose edge number and Euler characteristic are coprime. The classification establishes that such maps comprise three families: $\D_{2n}$-maps, $(\ZZ_{m}{:}\D_{4})$-maps, and $(\ZZ_{m}.§_4)$-maps, where $m$ is odd. Our classification is based on an explicit characterization obtained of finite almost Sylow-cyclic groups, associated with a shorter proof and explicit description of generators and relations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07033 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A classification of vertex-reversing maps with Euler characteristic coprime to the edge number Li, Cai Heng Liu, Luyi Yi, Hanyue Group Theory 05C25 A map is \emph{vertex-reversing} if it admits an arc-transitive automorphism group with dihedral vertex stabilizers. This paper classifies solvable vertex-reversing maps whose edge number and Euler characteristic are coprime. The classification establishes that such maps comprise three families: $\D_{2n}$-maps, $(\ZZ_{m}{:}\D_{4})$-maps, and $(\ZZ_{m}.§_4)$-maps, where $m$ is odd. Our classification is based on an explicit characterization obtained of finite almost Sylow-cyclic groups, associated with a shorter proof and explicit description of generators and relations. |
| title | A classification of vertex-reversing maps with Euler characteristic coprime to the edge number |
| topic | Group Theory 05C25 |
| url | https://arxiv.org/abs/2510.07033 |