Partial augmentations and Brauer character values of torsion units in group rings
Abstract
Description
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 $\text{\rm PSL}(2,p^{f})$.
16 pages, LateX. Thoroughly revised. Added references. Changed presentation of modular method. Lemma 5.6 replaced by Proposition 2.2
16 pages, LateX. Thoroughly revised. Added references. Changed presentation of modular method. Lemma 5.6 replaced by Proposition 2.2