Every group is the automorphism group of a graph with arbitrarily large genus
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912557098336256 |
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| author | Barbieri, Marco |
| author_facet | Barbieri, Marco |
| contents | We prove that, to every abstract group $G$, we can associate a sequence of graphs $Γ_n$ such that the automorphism group of $Γ_n$ is isomorphic to $G$ and the genus of $Γ_n$ is an unbounded function of $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_08747 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Every group is the automorphism group of a graph with arbitrarily large genus Barbieri, Marco Group Theory Combinatorics 05C10, 05C25 We prove that, to every abstract group $G$, we can associate a sequence of graphs $Γ_n$ such that the automorphism group of $Γ_n$ is isomorphic to $G$ and the genus of $Γ_n$ is an unbounded function of $n$. |
| title | Every group is the automorphism group of a graph with arbitrarily large genus |
| topic | Group Theory Combinatorics 05C10, 05C25 |
| url | https://arxiv.org/abs/2501.08747 |