Methods and problems of modern algebra.
(Methoden und Probleme der modernen Algebra.)

*(German)*Zbl 0799.01033Hans Zassenhaus was one of the outstanding mathematicians of the 20th century. The article in hand is a reprint of the inaugural lecture given by him at the university of Hamburg on August 1st, 1947. It should be regarded as a complement to the obituary of W. Plesken in the same volume as well as a historical document interesting for its own. First Zassenhaus characterized modern algebra by some essential features. He then selected problems from group theory, geometry of numbers, Lie algebras, lattice theory and the theory of nonlinear partial differential equations, to which he attached a great importance in the further development of mathematics. So for instance the determination of all finite simple groups, the classification of spatial groups of \(\mathbb{R}^ 4\) resp. the finding out of classes of nonlinear partial differential equations on the sphere having almost periodical solutions, are discussed by him. Zassenhaus himself made important contributions to many of the named topics. Finally there are 73 recommendations for further reading.

Reviewer: K.-H.Schlote (Leipzig)