Noether's problem for metacyclic p-groups

Let K be any field & G be a finite group. Let G act on the rational function field K(xg : g ∈ G) by K-automorphisms defined by g · xh = xgh for any g, h ∈ G. Denote by K(G) the fixed field K(xg : g ∈ G)G. Noether’s problem asks whether K(G) is rational (=purely transcendental) over K. An affirmative answer to Noether’s problem for metacyclic p-groups will be proved provided that K contains enough roots of unity