On the indecomposable involutive set-theoretic solutions of the Yang-Baxter equation of prime-power size

Abstract

We develop a method to construct all the indecomposable involutive non-degenerate set-theoretic solutions of the Yang-Baxter equation with a prime-power number of elements and cyclic permutation group. Moreover, we give a complete classification of the indecomposable ones having abelian permutation group and cardinality pq (where p and q are prime numbers not necessarily distinct).