Noether's problem and unramified Brauer groups

Akinari Hoshi, Ming-chang Kang, Boris E. Kunyavskii

Let $k$ be any field, $G$ be a finite group acing on the rational function field $k(x_g:g\in G)$ by $h\cdot x_g=x_{hg}$ for any $h,g\in G$. Define $k(G)=k(x_g:g\in G{)}^G$. Noether's…