Translator Disclaimer
June 2005 Geometric Generalization of Gaussian Period Relations with Application to Noether's Problem for Meta-Cyclic Groups
Ki-ichiro HASHIMOTO, Akinari HOSHI
Tokyo J. Math. 28(1): 13-32 (June 2005). DOI: 10.3836/tjm/1244208276

Abstract

We study Noether's problem over $\mathbb{Q}$ for meta-cyclic groups. This paper is an extension of the previous work [2], which was concerned with the cyclic group ${C_n}$ of order $n$. We shall give a simple description of the action of the normalizer of $C_n$ in $S_n$ to the function field $\mathbb{Q}(x_1,\ldots,x_n)$, in terms of the generators of the fixed field of $C_n$ given in [2]. Using this, we settle Noether's problem for the dihedral group of order $2n$ $(n \leq 6)$ and the Frobenius group of order $20$ with explicit construction of independent generators of the fixed fields. We shall also reconstruct some simple one-parameter families of cyclic and dihedral polynomials.

Citation

Download Citation

Ki-ichiro HASHIMOTO. Akinari HOSHI. "Geometric Generalization of Gaussian Period Relations with Application to Noether's Problem for Meta-Cyclic Groups." Tokyo J. Math. 28 (1) 13 - 32, June 2005. https://doi.org/10.3836/tjm/1244208276

Information

Published: June 2005
First available in Project Euclid: 5 June 2009

zbMATH: 1081.12002
MathSciNet: MR2149620
Digital Object Identifier: 10.3836/tjm/1244208276

Rights: Copyright © 2005 Publication Committee for the Tokyo Journal of Mathematics

JOURNAL ARTICLE
20 PAGES


SHARE
Vol.28 • No. 1 • June 2005
Back to Top