  This paper shows that every finite non-degenerate involutive set theoretic
solution (X,r) of the Yang-Baxter equation whose symmetric group has
cardinality which a cube-free number is a multipermutation solution.
  Some properties of finite braces are also investigated (Theorems 3, 5 and
11).
  It is also shown that if A is a left brace whose cardinality is an odd number
and (-a) b=-(ab) for all a, b A, then A is a two-sided brace and hence a
Jacobson radical ring. It is also observed that the semidirect product and the
wreath product of braces of a finite multipermutation level is a brace of a
finite multipermutation level.
