# On Noether's problem for cyclic groups of prime order

@article{Hoshi2014OnNP,
title={On Noether's problem for cyclic groups of prime order},
author={Akinari Hoshi},
journal={arXiv: Number Theory},
year={2014}
}
• A. Hoshi
• Published 2014
• Mathematics
• arXiv: Number Theory
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 $h(x_g)=x_{hg}$ for any $g,h\in G$. Noether's problem asks whether the invariant field $k(G)=k(x_g\,|\,g\in G)^G$ is rational (i.e. purely transcendental) over $k$. In 1974, Lenstra gave a necessary and sufficient condition to this problem for abelian groups $G$. However, even for the cyclic group $C_p$ of prime order $p$, it is unknown whether there exist infinitely many… Expand
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