  Let K be any field and G be a finite group. We will prove that, if K is any
field, p an odd prime number, and G is a non-abelian group of exponent p with
|G|=p^3 or p^4 satisfying [K(\zeta_p):K] <= 2, then K(G) is rational over K. We
will also show that K(G) is retract rational if G belongs to a much larger
class of p-groups. In particular, generic G-polynomials of G-Galois extensions
exist for these groups.
