Partial augmentations and Brauer character values of torsion units in group rings

Details Partial augmentations and Brauer character values of torsion units in group rings Partial augmentations and Brauer character values of torsion units in group rings

2006-12-15

arxiv.org/abs/math/0612429v2

Mathematics

Rings and Algebras

16 pages, LateX. Thoroughly revised. Added references. Changed presentation of modular method. Lemma 5.6 replaced by Propositi

Scientific paper

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

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