**Hans Fitting** was a German mathematician who is well-known for his results in group theory and Lie algebras.

- Friedrich Fitting is best known today for giving a proof, in 1931, that there are exactly 880 magic squares of order 4.
- This result appears in his paper Rein mathematische Behandlung des Problems der magischen Quadrate von 16 und von 64 Feldern Ⓣ(Pure mathematical treatment of the problem of magic squares of 16 and 64 squares) and is remarkable since these 880 magic squares had been given by Frenicle de Bessy in 1693 but no proof was found until Friedrich Fitting's 1931 paper appeared.
- From 1925 to 1932 Fitting studied mathematics, physics and philosophy at the Universities of Tübingen and Göttingen, where he was awarded his Ph.D. in 1932 for his work on group theory.
- Fitting achieved this in his dissertation Zur Theorie der Automorphismenringe Abelscher Gruppen und ihr Analogon bei nichtkommutativen Gruppen Ⓣ(On the theory of automorphism-rings of abelian groups and their analogs in non-commutative groups).
- Following his Ph.D., Fitting continued his research at the Mathematical Institutes of the Universities of Göttingen and Leipzig, funded by the "Notgemeinschaft der Deutschen Wissenschaften" (which can be translated loosely as the Emergency Association for German Science).
- Emmy Noether advised Fitting to apply for this grant and she had strongly supported his application.
- In April 1934 Fitting moved to Königsberg, where he worked as a research assistant and later as an assistant lecturer in mathematics.
- It was through contacting Richard Brauer that Emmy Noether was able to secure the position for Fitting.
- Fitting was not the only new mathematics appointment to Königsberg in April 1933 for Wilhelm Specht was appointed at the same time.
- Fitting habilitated at the Science Faculty of the University of Königsberg in April 1936 and on 1 November 1937 he was promoted to lecturer for mathematics.
- In his brief spell as a lecturer, Fitting led classes on a wide range of mathematical topics and distinguished himself, in particular, by his great attention to detail.
- As a mathematician Fitting followed a reflective, yet meticulous approach, which allowed him to fully explore his ideas and their consequences.
- Among the many mathematical achievements of Fitting we note that he gave a proof of the Remak-Krull-Schmidt theorem on the uniqueness of the direct product decomposition of groups into indecomposable subgroups, even for groups of operators.
- In his 33-page paper Die Determinantenideale eines Moduls Ⓣ(The determinant ideals of a module) (1936), the first part of his habilitation thesis, Fitting introduced what today are called 'Fitting ideals' of MMM.
- Also in this paper is the well-known 'Fitting's Lemma' which states that if AAA and BBB are two normal nilpotent subgroups of a group GGG with classes aaa and bbb respectively, then ABABAB is a nilpotent subgroup of class at most a+ba+ba+b.
- Today, as well as for Fitting's Lemma, he is remembered for the 'Fitting subgroup' which is used in the structure theory of finite groups: every finite group GGG possesses a unique largest normal nilpotent subgroup, the Fitting subgroup F(G)F(G)F(G).
- Since the factor group G/F(G)G/F(G)G/F(G) is non-trivial for finite groups GGG that are not nilpotent, this gives rise to the Fitting length of a finite group.
- On 6 June 1938, after a long illness, Fitting succumbed to bone cancer, aged only 31.

Born 13 November 1906, München Gladbach (now Mönchengladbach), Germany. Died 15 June 1938, Königsberg, Prussia, Germany (now Kaliningrad, Russia).

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Group Theory, Origin Germany

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive