On Noether’s problem for cyclic groups of prime order
On Noether’s problem for cyclic groups of prime order
Let $k$ be a field and $G$ be a finite group acting on the rational function field $k(x_{g}\mid g\in G)$ by $k$-automorphisms $h(x_{g})=x_{hg}$ for any $g,h\in G$. Noether’s problem asks whether the invariant field $k(G)=k(x_{g}\mid g\in G)^{G}$ is rational (i.e. purely transcendental) over $k$. In 1974, Lenstra gave a necessary …