Primitive set-theoretic solutions of the Yang–Baxter equation

To every involutive non-degenerate set-theoretic solution [Formula: see text] of the Yang–Baxter equation on a finite set there is naturally associated solvable permutation group acting text]. We prove that primitive this type prime order Moreover, then so-called determined by cycle length This solves problem recently asked A. Ballester-Bolinches. The result opens new perspective possible approach to classification all solutions.