Noether's problem for p-groups with a cyclic subgroup of index p2
Journal
Advances in Mathematics
Journal Volume
226
Journal Issue
1
Pages
218-234
Date Issued
2011
Author(s)
Abstract
Let K be any field and G be a finite group. Let G act on the rational function field K(xg:g∈G) by K-automorphisms defined by g.xh=xgh for any g,h∈G. Noether's problem asks whether the fixed field K(G)=K(xg:g∈G)G is rational (=purely transcendental) over K. We will prove that if G is a non-abelian p-group of order pn (n≥3) containing a cyclic subgroup of index p2 and K is any field containing a primitive pn-2-th root of unity, then K(G) is rational over K. As a corollary, if G is a non-abelian p-group of order p3 and K is a field containing a primitive p-th root of unity, then K(G) is rational. © 2010 Elsevier Inc.
Type
journal article