Cayley graphs and their growth functions for multivalued groups
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913857668120576 |
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| author | Bardakov, Valeriy G. Kozlovskaya, Tatyana A. Zonov, Matvei N. |
| author_facet | Bardakov, Valeriy G. Kozlovskaya, Tatyana A. Zonov, Matvei N. |
| contents | We define the Cayley graph and its growth function for multivalued groups. We prove that if we change a finite set of generators of multivalued group, or change the starting point, we get an equivalent growth function. We prove that if we take a virtually nilpotent group and construct a coset group with respect a finite group of authomorphisms, then this multivalued group has a polynomial growth. Also, we find a connection between this growth function and growth function of multivalued dynamics. It particular, it is obtained upper and lower bounds on growth functions of multivalued dynamics. We give a particular answer to a question of Buchstaber on polynomial growth of dynamics and a question of Buchstaber and Vesnin on growth functions of cyclically presented multivalued groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_18804 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cayley graphs and their growth functions for multivalued groups Bardakov, Valeriy G. Kozlovskaya, Tatyana A. Zonov, Matvei N. Group Theory We define the Cayley graph and its growth function for multivalued groups. We prove that if we change a finite set of generators of multivalued group, or change the starting point, we get an equivalent growth function. We prove that if we take a virtually nilpotent group and construct a coset group with respect a finite group of authomorphisms, then this multivalued group has a polynomial growth. Also, we find a connection between this growth function and growth function of multivalued dynamics. It particular, it is obtained upper and lower bounds on growth functions of multivalued dynamics. We give a particular answer to a question of Buchstaber on polynomial growth of dynamics and a question of Buchstaber and Vesnin on growth functions of cyclically presented multivalued groups. |
| title | Cayley graphs and their growth functions for multivalued groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2505.18804 |