Cayley graphs and their growth functions for multivalued groups

2025/05/24 by Bardakov, Valeriy G., Kozlovskaya, Tatyana A., Zonov, Matvei N.
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2505.18804

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.

Citations

• Multi-groups
• Multivalued groups and Newton polyhedron
• Symmetric skew braces and brace systems
• Dialgebras

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