Open Access
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 for meta-cyclic groups. This paper is an extension of the previous work [2], which was concerned with the cyclic group of order . We shall give a simple description of the action of the normalizer of in to the function field , in terms of the generators of the fixed field of given in [2]. Using this, we settle Noether's problem for the dihedral group of order and the Frobenius group of order 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

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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

Vol.28 • No. 1 • June 2005
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