On Higher Class Groups of Orders, by Manfred Kolster and Reinhard C. Laubenbacher

In this paper we study the torsion in odd-dimensional higher class groups of orders in semi-simple algebras over number fields. We show that the only torsion which can appear is for rational primes lying under prime ideals at which the order is not maximal, and we determine part of the structure of this torsion. These results are applied to integral group rings of symmetric groups and Dihedral groups. Also, we relate the structure of the higher odd-dimensional class groups of an integral group ring of a finite group to homomorphisms on its representation ring with values in twisted roots of unity, and, for abelian groups, also to homogeneous functions on the group.

Manfred Kolster <kolster@mcmaster.ca>
Reinhard C. Laubenbacher <reinhard@nmsu.edu>