Thursday, February 9, 15:45, 7.530

Mariano Serrano (Murcia)
On the Zassenhaus conjecture of direct products.

Abstract:
H.J. Zassenhaus conjectured that any unit of finite order and augmentation one in the integral group ring ZG of a finite group G is conjugate in the rational group algebra QG to an element of G. The Zassenhaus Conjecture found much attention and was proved for many series of groups, e.g. for nilpotent groups, groups possessing a normal Sylow subgroup with abelian complement or cyclic-by-abelian groups. However, there is no so much information about the conjecture for direct products. In this talk we present our recent results on the Zassenhaus Conjecture for the direct product GxA, where G is a Camina finite group and A is an abelian finite group.