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

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

2010-01-19

arxiv.org/abs/1001.3369v1

Acta Arithmetica, volume 149, issue 4, 2011, pages 347-359

Mathematics

Number Theory

Scientific paper

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 study some l-groups, where l is an odd prime number. In particular, together with [1] we will complete the study of realizable Steinitz classes for groups of 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

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