Otto Schreier
Encyclopedia
Otto Schreier was an Austria
n mathematician
who made major contributions in combinatorial group theory
and in the topology of Lie groups. He studied mathematics at the University of Vienna
and obtained his doctorate in 1923, under the supervision of Philipp Furtwängler
. He then moved to the University of Hamburg
.
Austria
Austria , officially the Republic of Austria , is a landlocked country of roughly 8.4 million people in Central Europe. It is bordered by the Czech Republic and Germany to the north, Slovakia and Hungary to the east, Slovenia and Italy to the south, and Switzerland and Liechtenstein to the...
n mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who made major contributions in combinatorial group theory
Combinatorial group theory
In mathematics, combinatorial group theory is the theory of free groups, and the concept of a presentation of a group by generators and relations...
and in the topology of Lie groups. He studied mathematics at the University of Vienna
University of Vienna
The University of Vienna is a public university located in Vienna, Austria. It was founded by Duke Rudolph IV in 1365 and is the oldest university in the German-speaking world...
and obtained his doctorate in 1923, under the supervision of Philipp Furtwängler
Philipp Furtwängler
Philipp Furtwängler was a German number theorist.He wrote an 1896 doctoral dissertation at the University of Göttingen on cubic forms , under Felix Klein...
. He then moved to the University of Hamburg
University of Hamburg
The University of Hamburg is a university in Hamburg, Germany. It was founded on 28 March 1919 by Wilhelm Stern and others. It grew out of the previous Allgemeines Vorlesungswesen and the Kolonialinstitut as well as the Akademisches Gymnasium. There are around 38,000 students as of the start of...
.
Results and concepts named after Otto Schreier
- Nielsen–Schreier theoremNielsen–Schreier theoremIn group theory, a branch of mathematics, the Nielsen–Schreier theorem is the statement that every subgroup of a free group is itself free. It is named after Jakob Nielsen and Otto Schreier.-Statement of the theorem:...
- Schreier refinement theoremSchreier refinement theoremIn mathematics, the Schreier refinement theorem of group theory states that any two normal series of subgroups of a given group have equivalent refinements....
- Artin–Schreier theorem
- Schreier's subgroup lemmaSchreier's subgroup lemmaSchreier's subgroup lemma is a theorem in group theory used in the Schreier–Sims algorithm and also for finding a presentation of a subgroup.-Definition:Suppose H is a subgroup of G, which is finitely generated with generating set S, that is, G = ....
- Schreier–Sims algorithm
- Schreier coset graph
- Schreier conjectureSchreier conjectureIn finite group theory, the Schreier conjecture asserts that the group of outer automorphisms of every finite simple group is solvable. It was proposed by Otto Schreier in 1926, and is now known to be true as a result of the classification of finite simple groups, but no simpler proof is known....