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Hans Zassenhaus's secondary education was at two schools in Hamburg, graduating from the Lichtwark Schule in 1930 and in the year entering the University of Hamburg. At first he studied mathematics and physics with the intention of specialising in atomic physics. However he had fine mathematics teachers in Artin and Hecke and, particularly Artin inspired him to undertake research in mathematics.
Zassenhaus studied for his doctorate under Artin's supervision. During this time he proved Zassenhaus's lemma, a beautiful result on subgroups which can be used to give a simple proof of the Jordan-Hölder theorem.
In his doctoral dissertation of 1934 he considered permutation groups whose elements are determined by the images of three points. These groups are called Zassenhaus groups today. In his dissertation Zassenhaus classified all 3-fold transitive Zassenhaus groups. These groups play an important role in the classification of finite simple groups coordinated by Gorenstein.
From 1934 to 1936 Zassenhaus worked at the University of Rostock and wrote his famous group theory text Lehrbuch der Gruppentheorie (1937) based on Artin's lectures at Hamburg. He became Artin's assistant at Hamburg in 1936. His habilitation of 1938 studied Lie rings of prime characteristic.
Zassenhaus found that a normal academic career was made impossible for him because of his intense dislike of the Nazi party. He worked on weather forecasting during World War II but, when offered the chair of mathematics at Bonn in 1943 he asked that he could postpone a decision until the end of the war.
After the war he did not accept the Bonn post, preferring that it went to someone who had lost their chair under the Nazis. He continued to work at Hamburg, spending session 1948-49 at Glasgow in Scotland, then, in 1949, he accepted a chair of mathematics at Montreal. Although he visited many other universities during the next 10 years, he remained in the post at Montreal until he moved to the University of Notre Dame in 1959. Five years later he accepted the post of research professor at Ohio State University and held this position until he retired.
We have mentioned his work in group theory and Lie rings above. The work on Lie rings extended to Lie algebras and he developed computational methods for studying them. In a long series of papers he applied Lie algebras to problems of theoretical physics.
His work on computational algebraic number theory seems to have started when he visited Caltec in 1959 and collaborated with Taussky-Todd. He put forward a programme to develop methods for computational number theory which, given an algebraic number field, involved calculating its Galois group, an integral basis, the unit group and the class group. He contributed himself in a major way to all four of these tasks.
Zassenhaus worked on a broad range of topics and, in addition to those mentioned above, he worked on nearfields, the theory of orders, representation theory, the geometry of numbers and the history of mathematics. He loved teaching and wrote several articles on the topic such as On the teaching of algebra at the pre-college level.
Article by: J J O'Connor and E F Robertson
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List of References (6 books/articles)
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| Mathematicians born in the same country
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| Honours awarded to Hans Zassenhaus (Click below for those honoured in this way) | |
| CMS Jeffery-Williams Prize | 1974 |
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