Characters of finite groups with dihedral Sylow 2-subgroups

Abstract

In this article, we give alternate proofs of some intermediate results in the Gorenstein-Walter classification [6] of groups with dihedral Sylow 2subgroups. These intermediate results will be applied in an alternate proof [ 1 ] of the entire classification by the first author. Our proofs rely only on elementary character theory and do not use block theory, but they are motivated by the related work of Brauer [2] and of Gorenstein and Walter [6, Propositions l-41, which was obtained by block theory. Now we describe the situation which will be assumed in the following sections and in the three theorems stated below. For elementary properties of groups with dihedral Sylow 2-subgroups the reader is referred to [S, Section 7.71.