Partial Augmentations and Brauer Character Values of Torsion Units in Group Rings

For a torsion unit u of the integral group ring ZG 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 S5 and the groups PSL(2, p ).