A problem on rational invariants

AbstractLet K = k(x1, x2,…, xt) where k is a field and x1, x2,…, xt are algebraically free over k. Let G be a finite group of k-automorphisms of K such that σxi = cix1ai1…xtait for each σ∈G, 1≤i≤t, where ci∈k, aij∈Z. The problem is: is KG=k(y1,y2,…,yt) for some y1,y2,…,yt∈K? The role of the coefficients ci is considered and determined explicity when G is cyclic of prime order. This role is of a cohomological nature. We also solve the stated problem in a very special case