NOETHER’S PROBLEM FOR CENTRAL EXTENSIONS OF METACYCLIC p-GROUPS
Let K be a field and G be a finite group. Let G act on the rational function field by K automorphisms defined by for any Denote by the fixed field Noether’s problem then asks whether is rational (i.e., purely transcendental) over K. In this paper, we prove the rationality of over K for almost all central extensions of metacyclic p-groups, with some conditions on the presence of suitable roots of unity in K.
Noether’s problem, rationality problem, metacyclic p-groups.