On the Wedderburn Structure of Some Integral Frobenius Group Rings Original Research Article

The complete structure of integral group rings is widely unknown, even in the simplest cases of finite groups. We approach this problem here for some classes of semilinear Frobenius groups over image-adic splitting rings. Our viewpoint is the Wedderburn structure of the image-adic group ring, i.e., the description of its projections into the Wedderburn components of the group algebra and the various congruence interlockings between the matrix entries. A remarkable feature is the appearance of (partial) Gaussian and jacobian sums as matrix entries. Previous work of Plesken and Kleinert provides some theoretical background.