  In this paper we show that all indecomposable nondegenerate set-theoretical
solutions to the Quantum Yang-Baxter equation on a set of prime order are
affine, which allows us to give a complete and very simple classification of
such solutions. This result is a natural application of the general theory of
set-theoretical solutions to the quantum Yang-Baxter equation. It is also a
generalization of the corresponding statement for involutive set-theoretical
solutions proved in an earlier paper of P.E. and A.S. with T.Schedler.
  In order to prove our main result, we use the classification theory developed
by the third author (based on the ideas of Lu, Yan, and Zhu) to reduce the
problem to a group-theoretical statement: a finite group with trivial center
generated by a conjugacy class of prime order is a subgroup of the affine
group. Unfortunalely, we did not find an elementary proof of this statement,
and our proof relies on the classification of outer automorphisms of finite
simple groups.
