The Zassenhaus conjecture
Group rings, units in group rings, torsion units in integral group rings, Zassenhaus conjectures.
In the mid 1960’s, the german mathematician Hans J. Zassenhaus, inspired by
Gram Higman’s thesis and the work of Ian Hughes and Kenneth R. Pearson, stated several
conjectures that changed radically the field of research in group rings. Since then many
papers have been published about these conjectures, where either an affirmative answer
is settled for some specific case, or some counterexamples are determined. Still, it is only
very recently that Florian Eisele and Leo Margolis, based on some joint work with Ángel
del Rı́o, have found a counterexample for the only conjecture which has been left open.
This fact motivated the writing of this dissertation.