  The Steinitz class of a number field extension K/k is an ideal class in the
ring of integers O_k of k, which, together with the degree [K:k] of the
extension determines the O_k-module structure of O_K. We call R_t(k,G) the
classes which are Steinitz classes of a tamely ramified G-extension of k. We
will say that those classes are realizable for the group G; it is conjectured
that the set of realizable classes is always a group.
  In this paper we will develop some of the ideas contained in arXiv:0910.5080
to obtain some results in the case of groups of even order. In particular we
show that to study the realizable Steinitz classes for abelian groups, it is
enough to consider the case of cyclic groups of 2-power degree.
