ALGB Seminar: Brecht Verbeken

17/04/2018 - 16:00

Title: Some results concerning the prime graph question for integral group rings

Abstract: After the counterexample to the first Zassenhaus conjecture [ZC1] (by Margolis-Eisele), the attention shifted to some "related problems", i.e. weaker versions of [ZC1]. Of particular interest is the so-called prime graph question [PQ], which states that the prime graph of a finite group G is equal to the prime graph of V(ZG), the normalized torsion units of the integral group ring. In contrast to [ZC1] there exists a reduction theorem for [PQ], which we will prove during this talk. This reduction theorem in mind, I will give some results on [PQ] for sporadic simple groups. Afterwards I will elaborate on the HeLP-method, which is our main tool to tackle [PQ], and show how we can use this method in a specific case.