Retract rationality and Noether's problem
Commutative Algebra
2007-05-23 v1 Rings and Algebras
Abstract
Let K be any field and G be a finite group. We will prove that, if K is any field, p an odd prime number, and G is a non-abelian group of exponent p with |G|=p^3 or p^4 satisfying [K(\zeta_p):K] <= 2, then K(G) is rational over K. We will also show that K(G) is retract rational if G belongs to a much larger class of p-groups. In particular, generic G-polynomials of G-Galois extensions exist for these groups.
Keywords
Cite
@article{arxiv.0704.1700,
title = {Retract rationality and Noether's problem},
author = {Ming-chang Kang},
journal= {arXiv preprint arXiv:0704.1700},
year = {2007}
}