Cayley graphs and their growth functions for multivalued groups
Abstract
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.
Cite
@article{arxiv.2505.18804,
title = {Cayley graphs and their growth functions for multivalued groups},
author = {Valeriy G. Bardakov and Tatyana A. Kozlovskaya and Matvei N. Zonov},
journal= {arXiv preprint arXiv:2505.18804},
year = {2025}
}