Klaus Wilhelm Roggenkamp Explained

Klaus Wilhelm Roggenkamp (24 December 1940 – 23 July 2021[1]) was a German mathematician, specializing in algebra.

Education and career

As an undergraduate, Roggenkamp studied mathematics from 1960 to 1964 at the University of Giessen.[2] There in 1967 he received his PhD. His thesis Darstellungen endlicher Gruppen in Polynombereichen (Representations of finite groups in polynomial integral domains) was written under the supervision of Hermann Boerner. As a postdoc Roggenkamp was at the University of Illinois at Urbana-Champaign, where he studied under Irving Reiner, and at the University of Montreal. After four years as a professor at Bielefeld University, he was appointed to the chair of algebra at the University of Stuttgart.[2]

Roggenkamp and Leonard Lewy Scott collaborated on a long series of papers on the groups of units of integral group rings, dealing with problems connected with the "integral isomorphism problem", which was proposed by Graham Higman in his 1940 doctoral dissertation at the University of Oxford.[3] [4] In 1986 Roggenkamp and Scott proved their most famous theorem (published in 1987 in the Annals of Mathematics). Their theorem states that given two finite groups

G

and

H

, if

G

is isomorphic to

H

then

G

is isomorphic to

H

, in the case where

G

and

H

are finite p-groups over the p-adic integers, and also in the case where

G

and

H

are finite nilpotent groups. Their 1987 paper also established a very strong form of a conjecture made by Hans Zassenhaus. The papers of Roggenkamp and Scott were the basis for most developments which followed in the study of finite groups of units of integral group rings.[2]

In 1988 Roggenkamp and Scott found a counterexample to another conjecture by Hans Zassenhaus — the conjecture was a somewhat strengthened form of the conjecture that the "integral isomorphism problem" always has an affirmative solution.[5] Martin Hertweck, partly building on the techniques introduced by Roggenkamp and Scott for their counterexample, published a counterexample to the conjecture that the "integral isomorphism problem" can always be solved affirmatively.[6] [7]

Roggenkamp was elected a member of the Akademie gemeinnütziger Wissenschaften zu Erfurt (Erfurt Academy of Useful Sciences) and was made an honorary member of Ovidius University of Constanța in Romania.

Selected publications

Articles

Books

as editor

Notes and References

  1. https://trauer.krzbb.de/traueranzeige/klaus-roggenkamp Klaus Roggenkamp
  2. Web site: May 2000. König, Steffen. Zimmermann, Alexander. Biography and appreciation on the occasion of Klaus Roggenkamp's 60th birthday.
  3. Graham. Higman . 1940. The units of group-rings. Proceedings of the London Mathematical Society. (2). 46. 231–248. 10.1112/plms/s2-46.1.231 .
  4. Hertweck, Martin. Unit groups of integral finite group rings with no noncyclic abelian finite subgroups. 2007. math.RT. 0704.0412.
  5. Scott: On a conjecture of Zassenhaus and beyond. In: Leonid A. Bokut', Yu L. Ershov, Aleksei I. Kostikin (eds.): Proceedings of the International Conference on Algebra. Dedicated to the Memory of A. I. Mal'cev (= Contemporary Mathematics. 131, 1). Volume 1. American Mathematical Society, Providence RI 1992,, pp. 325-343
  6. Web site: Collaborations. Leonard Scott, University of Virginia (faculty.virginia.edu).
  7. Martin Hertweck: A counterexample to the isomorphism problem for integral group rings. In: Annals of Mathematics. Series 2, Volume 154, No. 1, 2001, pp. 115-138, .

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Klaus Wilhelm Roggenkamp".

Except where otherwise indicated, Everything.Explained.Today is © Copyright 2009-2025, A B Cryer, All Rights Reserved. Cookie policy.