Noether's problem for the groups with a cyclic subgroup of index 4

Ming-chang Kang, Ivo M. Michailov, Jian Zhou

Let $G$ be a finite group and $k$ be a field. Let $G$ act on the rational function field $k(x_g:g\in G)$ by $k$-automorphisms defined by $g\cdot x_h=x_{gh}$ for any $g,h\in G$. Noe…