Cayley graphs with few automorphisms: the case of infinite groups
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866910375196229632 |
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| author | Leemann, Paul-Henry de la Salle, Mikael |
| author_facet | Leemann, Paul-Henry de la Salle, Mikael |
| contents | We characterize the finitely generated groups that admit a Cayley graph whose only automorphisms are the translations, confirming a conjecture by Watkins from 1976. The proof relies on random walk techniques. As a consequence, every finitely generated group admits a Cayley graph with countable automorphism group. We also treat the case of directed graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_06020 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Cayley graphs with few automorphisms: the case of infinite groups Leemann, Paul-Henry de la Salle, Mikael Group Theory Combinatorics 05E18, 05E30, 20B27, 05C25, 05C63 We characterize the finitely generated groups that admit a Cayley graph whose only automorphisms are the translations, confirming a conjecture by Watkins from 1976. The proof relies on random walk techniques. As a consequence, every finitely generated group admits a Cayley graph with countable automorphism group. We also treat the case of directed graphs. |
| title | Cayley graphs with few automorphisms: the case of infinite groups |
| topic | Group Theory Combinatorics 05E18, 05E30, 20B27, 05C25, 05C63 |
| url | https://arxiv.org/abs/2010.06020 |