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The Steinitz class of a number field extension K/k is an ideal class in thering of integers O_k of k, which, together with the degree [K:k] of theextension determines the O_k-module structure of O_K. We call R_t(k,G) theclasses which are Steinitz classes of a tamely ramified G-extension of k. Wewill say that those classes are realizable for the group G; it is conjecturedthat the set of realizable classes is always a group.  In this paper we will develop some of the ideas contained in arXiv:0910.5080to study some l-groups, where l is an odd prime number. In particular, togetherwith [1] we will complete the study of realizable Steinitz classes for groupsof order l^3. We will also give an alternative proof of the results of [1],based on class field theory.  [1] C. Bruche. Classes de Steinitz d'extensions non abeliennes de degre p^3.Acta Arith., 137(2):177-191, 2009

Steinitz classes of tamely ramified nonabelian extensions of odd prime power order