English

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 uu of the integral group ring ZG\mathbb{Z} G of a finite group GG, and a prime pp which does not divide the order of uu (but the order of GG), a relation between the partial augmentations of uu on the pp-regular classes of GG and Brauer character values is noted, analogous to the obvious relation between partial augmentations and ordinary character values. For non-solvable GG, consequences concerning rational conjugacy of uu to a group element are discussed, considering as examples the symmetric group S5S_{5} and the groups PSL(2,pf)\text{\rm PSL}(2,p^{f}).

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