2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/127334Let 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(ζ_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.Commutative AlgebraRings and Algebras12F12, 13A50, 11R32, 14E08text