Noether's Problem on Semidirect Product Groups

Huah Chu, Shang Huang

Let $K$ be a field, $G$ a finite group. Let $G$ act on the function field $L=K(x_{\sigma }:\sigma \in G)$ by $\tau \cdot x_{\sigma }=x_{\tau \sigma }$ for any $\sigma ,\tau \in G$. Denote the fixed field of the action b…