A family of solutions of the Yang–Baxter equation

A new method to construct involutive non-degenerate set-theoretic solutions (Xn,r(n))(Xn,r(n)) of the Yang–Baxter equation, for any positive integer n  , from a given solution (X,r)(X,r) is presented. Furthermore, the permutation group G(Xn,r(n))G(Xn,r(n)) associated with the solution (Xn,r(n))(Xn,r(n)) is isomorphic to a subgroup of G(X,r)G(X,r), and in many cases G(Xn,r(n))≅G(X,r)G(Xn,r(n))≅G(X,r).