ALGB Seminar: Leo Margolis

The Zassenhaus Conjecture I - An Introduction

Abstract:
Hans J. Zassenhaus conjectured in 1974 that any unit of finite order in the integral group ring of a finite group G is conjugate in the rational group algebra to an element of the form ±g for some g ∈ G. Though proven e.g. for nilpotent or cyclic-by-abelian groups the conjecture does not hold in general and in a series of two talks I am going to present the first counterexamples recently found in collaboration with F. Eisele. In this first, non-technical lecture I am going to discuss the historic background of the conjecture and its connection to other problems in the field, many of which are still waiting to be solved.