The thesis discussed "nicht fortsetzbare Potenzreihen" (discontinuous power series), and was written under the direction of Helmut Wielandt.
When Wielandt moved to the University of Tübingen in April 1951, Huppert followed him later in the year, and gained his doctorate (as Wielandt's first doctoral student) with the work "Produkte von paarweise vertauschbaren zyklischen Gruppen" (products of pairwise permutable cyclic groups), in which he showed, among other things, that such groups were supersoluble.
The focus of the dissertation was very close to Wielandt's interests at the time, whose 1951 work shows that the product of pairwise permutable nilpotent groups is solvable.
Huppert spent the years 1963/64 as a visiting professor at the University of Illinois at Urbana-Champaign and at the California Institute of Technology (Caltech) in Pasadena.
In 1984, Huppert founded, together with Gerhard Michler, the first Deutsche Forschungsgemeinschaft priority programme in Mathematics at the German universities of Aachen, Bielefeld, Essen and Mainz.