Some families of finite groups and their rings of invariants
The Steinitz class of a number field extension is an ideal class in the ring of integers of , which, together with the degree of the extension determines the -module structure of . We denote by the set of classes which are Steinitz classes of a tamely ramified -extension of . We will say that those classes are realizable for the group ; 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 [7] to obtain some...
Nous déterminons sous certaines hypothèses, un système fondamental d’unités du corps non pur et de son sous-corps quadratique, où est solution du polynômeavec , , , , , non nuls.
We show that a cubic algebraic integer over a number field with zero trace is a difference of two conjugates over of an algebraic integer. We also prove that if is a normal cubic extension of the field of rational numbers, then every integer of with zero trace is a difference of two conjugates of an integer of if and only if the adic valuation of the discriminant of is not