Modüler temsiller ve tek terimli burnside halkaları

ABSTRACTMODULAR REPRESENTATIONS AND MONOMIALBURNSIDE RINGSOlcay CoşkunsM.S. in MathematicsSupervisors: Assoc. Prof. Dr. Laurence J. Barker andAsst. Prof. Dr. Ergün Yalşınu cAugust, 2004We introduce canonical induction formulae for some character rings of a finitegroup, some of which follows from the formula for the complex character ringconstructed by Boltje. The rings we will investigate are the ring of modularcharacters, the ring of characters over a number field, in particular, the fieldof real numbers and the ring of rational characters of a finite p−group. Wealso find the image of primitive idempotents of the algebra of the complex andmodular character rings under the corresponding canonical induction formulae.The thesis also contains a summary of the theory of the canonical inductionformula and a review of the induction theorems that are used to construct theformulae mentioned above.Keywords: Canonical induction, modular characters, real characters, rationalcharacters of p−groups, primitive idempotents.iii