CONSTRUCTION AND CLASSIFICATION OF SOME GALOIS MODULES

JAN MINAC JOHN SWALLOW

Abstract. In our previous paper we describe the Galois module structures of pth-power class groups K^{×}/K^{×p}, where K/F is a cyclic extension of degree p over a field F containing a primitive pth root of unity. Our description relies upon arithmetic invariants associated with K/F. Here we construct field extensions K/F with prescribed arithmetic invariants, thus completing our classification of Galois modules K^{×}/K^{×p}.