On the surjectivity of some trace maps (Q1327507)

Let \(K\) be a commutative ring and let \(G\) be a finite group acting on \(K\) by ring-automorphisms. The author studies the trace map \(\text{tr}_G : K \to K^G\), \(x \mapsto \sum_{g \in G} g(x)\). His main result is: The trace map \(\text{tr}_G : K \to K^G\) is surjective if and only if the trace maps \(\text{tr}_P : K \to K^P\) are surjective, for every prime order subgroup \(P\) of \(G\).