A new approach to the genus spectra of abelian $p$-groups
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866917584590340096 |
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| author | Chen, Haimiao Li, Yang |
| author_facet | Chen, Haimiao Li, Yang |
| contents | Given a finite group $G$, the {\it genus spetrum} ${\rm sp}(G)$ of $G$ is the set of integers $g\geq 0$ such that $G$ can act faithfully on an orientable closed surface of genus $g$ by orientation-preserving homeomorphisms. The determination of ${\rm sp}(G)$ is a classical topic and has a long history, but progress is lacked. In this paper, when $G$ is an abelian $p$-group with $p>2$, we propose a new approach to ${\rm sp}(G)$, giving a structural description for ${\rm sp}(G)$ in terms of a function which can be computed in finitely many steps. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2204_01990 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A new approach to the genus spectra of abelian $p$-groups Chen, Haimiao Li, Yang Group Theory Combinatorics 20K01, 57M60, 05E18 Given a finite group $G$, the {\it genus spetrum} ${\rm sp}(G)$ of $G$ is the set of integers $g\geq 0$ such that $G$ can act faithfully on an orientable closed surface of genus $g$ by orientation-preserving homeomorphisms. The determination of ${\rm sp}(G)$ is a classical topic and has a long history, but progress is lacked. In this paper, when $G$ is an abelian $p$-group with $p>2$, we propose a new approach to ${\rm sp}(G)$, giving a structural description for ${\rm sp}(G)$ in terms of a function which can be computed in finitely many steps. |
| title | A new approach to the genus spectra of abelian $p$-groups |
| topic | Group Theory Combinatorics 20K01, 57M60, 05E18 |
| url | https://arxiv.org/abs/2204.01990 |