  To every involutive non-degenerate set-theoretic solution $(X,r)$ of the
Yang-Baxter equation on a finite set $X$ there is a naturally associated finite
solvable permutation group ${\mathcal G}(X,r)$ acting on $X$. We prove that
every primitive permutation group of this type is of prime order $p$. Moreover,
$(X,r)$ is then a so called permutation solution determined by a cycle of
length $p$. This solves a problem recently asked by A. Ballester-Bolinches. The
result opens a new perspective on a possible approach to the classification
problem of all involutive non-degenerate set-theoretic solutions.

Rings and Algebras;Group Theory