Partial augmentations and Brauer character values of torsion units in group rings
Rings and Algebras
2007-05-23 v2 Representation Theory
Abstract
For a torsion unit of the integral group ring of a finite group , and a prime which does not divide the order of (but the order of ), a relation between the partial augmentations of on the -regular classes of and Brauer character values is noted, analogous to the obvious relation between partial augmentations and ordinary character values. For non-solvable , consequences concerning rational conjugacy of to a group element are discussed, considering as examples the symmetric group and the groups .
Keywords
Cite
@article{arxiv.math/0612429,
title = {Partial augmentations and Brauer character values of torsion units in group rings},
author = {Martin Hertweck},
journal= {arXiv preprint arXiv:math/0612429},
year = {2007}
}
Comments
16 pages, LateX. Thoroughly revised. Added references. Changed presentation of modular method. Lemma 5.6 replaced by Proposition 2.2