On the Wedderburn structure of some integral Frobenius group rings (Q1345919)

Let \(K\) be an unramified extension of the field \(\mathbb{Q}_p\) of rational \(p\)-adic numbers, \(R\) the ring of integers of \(K\) and \(S = R[\root p \of {1}]\). In the paper the integral group rings \(SG\) and \(RG\) are investigated for linear Frobenius groups and for semilinear Frobenius groups \(G\) of maximal type. A precise description of the Wedderburn components of the group rings \(SG\) and \(RG\), in particular in the linear case, is given by using Gaussian and Jacobian sums. The investigation is essentially based on the classification of graduated orders [\textit{W. Plesken}, Group rings of finite groups over \(p\)-adic integers. Lect. Notes Math. 1026 (1983; Zbl 0537.20002)] and Zassenhaus' Classification Theorem for semilinear Frobenius groups of maximal type.