Otto Schreier

Otto Schreier ( born March 3, 1901 in Vienna, † June 2, 1929 in Hamburg) was an Austrian mathematician who worked on combinatorial group theory and was known among other things with the set of Nielsen - Schreier.

Schreier studied from 1920 at the University of Vienna with Wilhelm Wirtinger, Philipp Furtwängler, Hans Hahn, Kurt Reidemeister, Leopold Vietoris, Josef Lense. In 1923 he was at Furtwängler doctorate (On the expansion of groups). In 1926 he habilitated with Emil Artin at the University of Hamburg ( The subgroups of the free group. Treatises of the Mathematics Department of the University of Hamburg, Volume 5, 1927, pages 172-179 ), where he lectured even before his habilitation.

In 1928 he became a professor at the University of Rostock. He held in the winter semester lectures simultaneously in Hamburg and Rostock, but fell ill in December 1928 severely from sepsis, of which he died six months later.

Schreier came to Group Theory by Kurt Reidemeister and first examined in 1924 node groups following the work of Max Dehn. His best known work is his habilitation thesis on the subgroups of free groups, in which he generalizes results of Reidemeister on the normal subgroups. He proved that the subgroups of free groups are even free, a set of Jakob Nielsen ( 1921) generalized ( set of Nielsen - Schreier ). In 1927 he showed that the topological fundamental group of classical Lie groups is abelian. In 1928, he improved the set of Jordan - Hölder (About the Jordan - Hölder theorem. Treatises Mathem. Seminar University of Hamburg, Bd.6, 1930, pages 300-302, see figure). With Emil Artin, he proved the theorem of Artin - Schreier for the characterization of real closed body ( Algebraic construction of real body. Treatises Mathem. Seminar Hamburg, Volume 5, 1927).

The Schreier conjecture of group theory states that the group of outer automorphisms of any finite simple group is solvable ( the conjecture follows from the Klassifikationstheorem of finite simple groups, which is proved by a general conviction ).

Emanuel Sperner received his doctorate in Hamburg with him in 1928.

Writings

• Over recent investigations in the theory of continuous groups. Annual Report DMV, Bd.37 1928, according to a held at the Annual Meeting of the DMV in September 1926 lecture.