arXiv math/06124292006-12math.RAmath.RT

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

Martin Hertweck

备注：: 16 pages, LateX. Thoroughly revised. Added references. Changed presentation of modular method. Lemma 5.6 replaced by Proposition 2.2

英文摘要：

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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