On indecomposable IYB-groups and their primes

Abstract

This paper investigates the mathematical properties of IYB-groups, particularly focusing on the set of primes that divide the cardinality of finite IYB-groups associated to indecomposable set-theoretic solutions of the Yang-Baxter equation. We establish a direct relationship between the primes that divide the cardinality of an IYB-group and those that divide the cardinality of the finite set on which the solution is defined. From this, we derive an upper bound for the primes dividing these IYB-groups for indecomposable solutions.