Noether's problem for some meta-abelian groups of small degree

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Noether's problem for some meta-abelian groups of small degree

Akinari Hoshi

Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 81, Number 1 (2005), 1-6.

Abstract

In this note we solve Noether's problem over $\mathbf{Q}$ for some meta-abelian groups of small degree $n$. Let $G$ be a subgroup of the group of one-dimensional affine transformations on $\mathbf{Z}/n\mathbf{Z}$ which contains $\mathbf{Z}/n\mathbf{Z}$. For $n=9,10,12,14,15$, we show that Noether's problem for $G$ has an affirmative answer by constructing an explicit transcendental basis of the fixed field over $\mathbf{Q}$.

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Primary Subjects: 12F12

Secondary Subjects: 11R32, 12F10

Keywords: Inverse Galois problem; generic polynomial; affine transformation group

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.pja/1116442081
Mathematical Reviews number (MathSciNet): MR2068482
Zentralblatt MATH identifier: 1083.12002
Digital Object Identifier: doi:10.3792/pjaa.81.1

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