Hans Fitting (mathematician)
Hans Fitting (born November 13, 1906 in Mönchengladbach ; † June 15, 1938 in Königsberg (Prussia) ) was a German mathematician who dealt with algebra and developed important concepts in the theory of finite groups before his untimely death .
Live and act
Hans Fitting was the son of a mathematics high school teacher and studied mathematics, physics and philosophy in Tübingen and Göttingen . There he received his doctorate in 1931 under Emmy Noether ( The theory of automorphism rings of Abelian groups and their analogue in non-commutative groups , Mathematische Annalen, Vol. 37, 1932, p. 514). With a grant from the Notgemeinschaft der Deutschen Wissenschaft he conducted research in Göttingen and Leipzig from 1932 to 1934 . From 1934 he was an assistant in Königsberg , where he completed his habilitation in 1936 and lectured as a private lecturer from 1937 . He died of bone cancer.
Fitting proved structure theorems for finite groups, where the fitting subgroup is named after him. It is generated by all normal nilpotent subgroups of a finite group G (the product of which is again normal and nilpotent according to Fitting's theorem). This maximal nilpotent normal subgroup determines in a certain way the structure of solvable finite groups G. A corresponding role in general finite groups is played by the generalized fitting subgroup introduced by Helmut Bender in the 1970s .
The fitting decomposition of Lie algebras is named after fitting . The fitting lemma is a fundamental theorem of algebra, which is formulated in various ways, but is usually given in the form of a theorem for endomorphisms of modules . It then states that an endomorphism of an indecomposable module of finite length over a ring is either nilpotent or an automorphism .
Fonts
- Contributions to the theory of groups of finite order , annual report DMV 1938
- Purely mathematical treatment of the problem of the Latin squares of 16 and 64 fields , DMV annual report 1931
literature
- Maximilian Pinl: Fitting, Hans. In: New German Biography (NDB). Volume 5, Duncker & Humblot, Berlin 1961, ISBN 3-428-00186-9 , p. 217 f. ( Digitized version ).
Web links
- Hans Zassenhaus In memory of Hans Fitting , Annual Report DMV Vol. 49, 1939
- Fitting Lemma at Planet Math
| personal data | |
|---|---|
| SURNAME | Fitting, Hans |
| BRIEF DESCRIPTION | German mathematician |
| DATE OF BIRTH | November 13, 1906 |
| PLACE OF BIRTH | Mönchengladbach |
| DATE OF DEATH | June 15, 1938 |
| Place of death | Königsberg (Prussia) |