On the structure of some group codes.
Let be a finite nonabelian group, its associated integral group ring, and its augmentation ideal. For the semidihedral group and another nonabelian 2-group the problem of their augmentation ideals and quotient groups is deal with. An explicit basis for the augmentation ideal is obtained, so that the structure of its quotient groups can be determined.
From a paper by A. Angelakis and P. Stevenhagen on the determination of a family of imaginary quadratic fields having isomorphic absolute Abelian Galois groups , we study any such issue for arbitrary number fields . We show that this kind of property is probably not easily generalizable, apart from imaginary quadratic fields, because of some -adic obstructions coming from the global units of . By restriction to the -Sylow subgroups of and assuming the Leopoldt conjecture we show that the...
In this paper we consider completely decomposable torsion-free groups and we determine the subgroups which are ideals in every ring over such groups.