On the abelian groups which occur as Galois cohomology groups of global unit groups

Abstract

For any finite group G and integer i, let ${\mathcal{H}}^i(G)$ be the set of all the isomorphism classes of the Galois cohomology groups ${\hat{H}}^i(K/k,E_K)$, where K/k runs over all the unramified G-extension of number fields and E_K denotes the global unit group of K. We will determine ${\mathcal{H}}^i(G)$ for i=0,1,2, and 4 in the case where G is a finite p-group.