nLab Otto Schreier

Otto Schreier (1901–1929) was a German algebraist born in Vienna famous for his work in combinatorial group theory (Nielsen–Schreier method and HNN-extensions). His 1926 article on extensions of groups contains ideas of nonabelian cohomology and pseudofunctors; nowadays this is called Schreier’s theory of (nonabelian) extensions. The work has been completed by Eilenberg and Mac Lane in a series of three papers in the late 1940s. Higher analogues of Schreier’s theory were studied by L. Breen. Schreier’s theory can be also extended to some other algebraic structures, see e.g. nonabelian Lie algebra cohomology.

See biographical and some mathematical data at the MacTutor biography. For more on the mathematical side see

• W. Magnus, The history of combinatorial group theory: a case study in the history of ideas

Selected writings

Proving the Nielsen-Schreier theorem on subgroups of free groups and introducing the notion of what came to be known as the amalgamated free product of groups:

• Otto Schreier, Die Untergruppen der freien Gruppen, Abh. Math. Semin. Univ. Hambg. 5 (1927) 161–183 [doi:10.1007/BF02952517]

Related entries

• Schreier theory