### Mathematisch-Naturwissenschaftliche Fakultät

## Institut für Mathematik

### Fachgebiet: Darstellungstheorie endlicher Gruppen

Betreuer: Prof. Dr. Reinhard Knörr

**Dipl.-Math.** **Frieder** **Ladisch**

(e-mail: frieder.ladisch@uni-rostock.de )

*Character Correspondences in Finite Groups*

In the theory of linear representations of finite groups and their
characters, methods for relating characters of a group with characters
of one of its subgroups are desirable. In this thesis, we consider a
character bijection between characters of a group lying over a fixed
character of a normal subgroup, and similar defined characters of a
subgroup. This situation occurs in many applications, for example in
the proof of character correspondences found by Dade and Isaacs. With
the techniques developed here, we can give significantly more
transparent proofs of these results. We also get generalizations
concerning modular representation theory and derive additional
properties of the Isaacs correspondence, in particular that it
preserves Schur indices.