turkmath.org

In 1992, Dress, Siebeneicher and Yoshida introduced the Frobenius-Wielandt morphism (FW morphism), defined from the Burnside ring of a cyclic group C to the Burnside ring of a finite group G of order |C|. A remark in their article indicates that their intention was "to give a precise conceptual interpretation of the observation that many elementary group-theoretic results can be derived from the fact that various invariants of an arbitrary group are closely related to the same invariant evaluated for the cyclic group C". Among other properties, they investigated the relation of the FW morphism with the operations of restriction, induction, inflation and fixed points. In this talk we will see what can be said about the relation of the FW morphism with other operations related to the Burnside ring, especifically: tensor induction and deflation.