# Hans Fitting

Hans Fitting ( born November 13, 1906 in Moenchengladbach, † June 15, 1938 in Königsberg ( Prussia) ) was a German mathematician who dealt with algebra and developed important concepts of the theory of finite groups before his untimely death.

## Life and work

Hans Fitting was the son of a maths school teacher and studied mathematics, physics and philosophy in Tübingen and Göttingen. There he received his doctorate in 1931 at Emmy Noether ( The theory of Automorphismenringe abelian groups and its analogue in non-commutative groups, Mathematische Annalen, Bd.37, 1932, S.514 ). With a grant from the Emergency Association of German Science 1932-1934, he conducted research in Göttingen and Leipzig. From 1934 he was an assistant in Königsberg, where he habilitated in 1936 and held lectures in 1937 as a lecturer. He died of bone cancer.

Fitting proving 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 the set of fitting again is normal and nilpotent ). This maximal nilpotent normal subgroup determines in some way the structure of solvable finite groups G. A similar role in general finite groups plays the generalized Fitting subgroup, which was introduced in the 1970s by Helmut Bender.

After fitting, the fitting decomposition of Lie algebras is named. The fitting lemma is a fundamental theorem of algebra, which is formulated differently, but is usually given in the form of a set of modules for Endomorphismenen. He then states that an endomorphism of an indecomposable module of finite length over a ring is either nilpotent or an automorphism.

## Writings

- Contributions to the theory of groups of finite order, DMV Annual Report 1938
- Pure mathematical treatment of the problem of Latin squares of 16 and 64 fields, " Annual Report 1931 DMV