Noether's problem for p-groups with three generators

Yin Chen

Let $p$ be an odd prime and $G$ be a nonabelian group of order $p^n$ with the presentation $$<α,β,γ\mid α^{p^{a}}=β^{p^{b}}=γ^{p^{c}}=1, [α,γ]=1,[γ,β]=α^{p^{r}},[α,β]=γ^{p^{e}}>,…