Retract rationality and Noether's problem

2007/04/13 by Kang, Ming-chang
#11R32 #12F12 #13A50 #14E08 #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.0704.1700

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|=p³ or p⁴ satisfying [K(ζ_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.

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