Noether's problem for some meta-abelian groups of small degree
Hoshi, Akinari
Proc. Japan Acad. Ser. A Math. Sci., Tome 81 (2005) no. 3, p. 1-6 / Harvested from Project Euclid
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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 $\mathbf{Q}$.
Publié le : 2005-01-14
Classification:  Inverse Galois problem,  generic polynomial,  affine transformation group,  12F12,  11R32,  12F10 
@article{1116442081,
     author = {Hoshi, Akinari},
     title = {Noether's problem for some meta-abelian groups of small degree},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {81},
     number = {3},
     year = {2005},
     pages = { 1-6},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1116442081}
}

Hoshi, Akinari. Noether's problem for some meta-abelian groups of small degree. Proc. Japan Acad. Ser. A Math. Sci., Tome 81 (2005) no. 3, pp.  1-6. http://gdmltest.u-ga.fr/item/1116442081/