Year: 2013
Type: preprint
Abstract: Let $p$ be an odd prime and $G$ be a nonabelian group of order $p^{n}$ with the presentation $$,$$ where $n>a\geq b\geq c\geq 1$. Let $k$ be a field containing a primitive $p^{a}$-th root of unity and $G$ act on the rational function field $k(x_{h}:h\in G)$ by $g\cdot x_{h}=x_{gh}$ for all $g,h\in G$. In this note, we prove that the fixed field $k(G)=k(x_{h}:h\in G)^{G}$ is rational over $k$. As a corollary, we prove that if $k$ contains a primitive $p^{4}$-th root of unity and $G$ is a nonabelian group of order $p^{5}$ generated by three elements, then $k(G)$ is rational over $k$.
Source: arXiv (Cornell University)
Author: Chen, Yin
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1805358116