• Corpus ID: 119651574

Noether's problem for p-groups of order p^{5}

@article{Chen2013NoethersPF,
  title={Noether's problem for p-groups of order p^\{5\}},
  author={Yin Chen},
  journal={arXiv: Algebraic Geometry},
  year={2013}
}
  • Yin Chen
  • Published 2 September 2013
  • Mathematics
  • arXiv: Algebraic Geometry
Let $k$ be any field, $p>3$ be any prime number and $G$ be a nonabelian $p$-group of order $p^{5}$. Consider the action of $G$ on the rational function field $k(x_{h}:h\in G)$ by $g\cdot x_{h}=x_{gh}$ for all $g,h\in G$. Let $e$ be the exponent of $G$. Noether's problem asks whether the fixed field $k(G)=k(x_{h}:h\in G)^{G}$ is rational (i.e., purely transcendental) over $k$. In this paper, we will prove that if $G$ does not belong to the isoclinic family $\Phi_{10}$ in James's classification… 

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