Degree three unramified cohomology groups and Noether's problem for groups of order $243$

Akinari Hoshi, Ming-chang Kang, Aiichi Yamasaki

Let $k$ be a field and $G$ be a finite group acting on the rational function field $k(x_g:g\in G)$ by $k$-automorphisms defined as $h(x_g)=x_{hg}$ for any $g,h\in G$. We denote t…