Abstract
Given an irreducible character χ of a finite group G the problem is how to calculate the Schur Index of χ over a number field. By results of Brauer one can restrict oneself to solvable groups of a very special type, and by means of global class field theory the problem can be reduced to the case where the ground field is a local field. We also use the concept of a k-primitive character which was introduced by Roquette. The main part of this paper then deals with the calculation of Schur Indices of irreducible characters over p-adic fields. Finally, we mention how two well-known results of Solomon and Fong can be derived from our considerations.
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