Otto Schreier
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Otto Schreier (3 March 1901 in
Vienna en, Viennese , iso_code = AT-9 , registration_plate = W , postal_code_type = Postal code , postal_code = , timezone = CET , utc_offset = +1 , timezone_DST ...
,
Austria Austria, , bar, Östareich officially the Republic of Austria, is a country in the southern part of Central Europe, lying in the Eastern Alps. It is a federation of nine states, one of which is the capital, Vienna, the most populous ...
– 2 June 1929 in
Hamburg Hamburg (, ; nds, label=Hamburg German, Low Saxon, Hamborg ), officially the Free and Hanseatic City of Hamburg (german: Freie und Hansestadt Hamburg; nds, label=Low Saxon, Friee un Hansestadt Hamborg),. is the List of cities in Germany by popul ...
,
Germany Germany, officially the Federal Republic of Germany (FRG),, is a country in Central Europe. It is the most populous member state of the European Union. Germany lies between the Baltic and North Sea to the north and the Alps to the sou ...
) was a
Jewish-Austrian The history of the Jews in Austria probably begins with the exodus of Jews from Judea under Roman occupation. Over the course of many centuries, the political status of the community rose and fell many times: during certain periods, the Jewis ...
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
who made major contributions in
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. It is much used in geometric topology, the fundamental group of a simplicial complex having in a nat ...
and in the topology of
Lie groups In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the addi ...
.


Life

His parents were the architect Theodor Schreier (1873-1943) and his wife Anna (b. Turnau) (1878-1942). From 1920 Otto Schreier studied at the University of Vienna and took classes with Wilhelm Wirtinger, Philipp Furtwängler, Hans Hahn, Kurt Reidemeister,
Leopold Vietoris Leopold Vietoris (; ; 4 June 1891 – 9 April 2002) was an Austrian mathematician, World War I veteran and supercentenarian. He was born in Radkersburg and died in Innsbruck. He was known for his contributions to topology—notably the Mayer–V ...
, and Josef Lense. In 1923 he obtained his
doctorate A doctorate (from Latin ''docere'', "to teach"), doctor's degree (from Latin ''doctor'', "teacher"), or doctoral degree is an academic degree awarded by universities and some other educational institutions, derived from the ancient formalism '' ...
, under the supervision of Philipp Furtwängler, entitled ''On the expansion of groups (Über die Erweiterung von Gruppen)''. In 1926 he completed his
habilitation Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including ...
with Emil Artin at the University of Hamburg ''(Die Untergruppen der freien Gruppe. Abhandlungen des Mathematischen Seminars der Universität Hamburg, Band 5, 1927, Seiten 172–179)'', where he had also given lectures before. In 1928 he became a professor at the University of Rostock. He gave lectures in Hamburg and Rostock at the same time in the winter semester but fell seriously ill from sepsis in December 1928, of which he died six months later. His daughter Irene was born a month after his death. His wife Edith (née Jakoby) and daughter were able to flee to the United States in January 1939. His daughter became a pianist and married the American mathematician
Dana Scott Dana Stewart Scott (born October 11, 1932) is an American logician who is the emeritus Hillman University Professor of Computer Science, Philosophy, and Mathematical Logic at Carnegie Mellon University; he is now retired and lives in Berkeley, C ...
(born 1932), whom she had met in Princeton. Otto Schreier's parents were murdered in the
Theresienstadt Theresienstadt Ghetto was established by the SS during World War II in the fortress town of Terezín, in the Protectorate of Bohemia and Moravia ( German-occupied Czechoslovakia). Theresienstadt served as a waystation to the extermination camp ...
concentration camp as part of the Holocaust.


Scientific contributions

Schreier was introduced to group theory by Kurt Reidemeister and first examined knot groups in 1924 following work by
Max Dehn Max Wilhelm Dehn (November 13, 1878 – June 27, 1952) was a German mathematician most famous for his work in geometry, topology and geometric group theory. Born to a Jewish family in Germany, Dehn's early life and career took place in Germany. H ...
. His best-known work is his habilitation thesis on the subgroups of free groups, in which he generalizes the results of Reidemeister about normal subgroups. He proved that subgroups of free groups themselves are free, generalizing a theorem by Jakob Nielsen (1921). In 1927 he showed that the topological fundamental group of a classical Lie group is abelian. In 1928 he improved Jordan-Hölder's theorem. With
Emil Artin Emil Artin (; March 3, 1898 – December 20, 1962) was an Austrian mathematician of Armenian descent. Artin was one of the leading mathematicians of the twentieth century. He is best known for his work on algebraic number theory, contributing ...
, he proved the
Artin-Schreier theorem In mathematics, a real closed field is a field ''F'' that has the same first-order properties as the field of real numbers. Some examples are the field of real numbers, the field of real algebraic numbers, and the field of hyperreal numbers. Def ...
characterizing Real closed fields. The Schreier conjecture of group theory states that the group of external automorphisms of any finite simple group is solvable (the conjecture follows from the classification theorem of finite simple groups, which is generally accepted). With Emanuel Sperner, he wrote an introductory textbook on linear algebra, which was well-known in German-speaking countries for a long time.


Significance of the Artin–Schreier theorem

According to
Hans Zassenhaus Hans Julius Zassenhaus (28 May 1912 – 21 November 1991) was a German mathematician, known for work in many parts of abstract algebra, and as a pioneer of computer algebra. Biography He was born in Koblenz in 1912. His father was a historian and ...
:


Results and concepts named after Otto Schreier

*
Nielsen–Schreier theorem In group theory, a branch of mathematics, the Nielsen–Schreier theorem states that every subgroup of a free group is itself free. It is named after Jakob Nielsen and Otto Schreier. Statement of the theorem A free group may be defined from a ...
* Schreier refinement theorem *
Artin–Schreier theorem In mathematics, a real closed field is a field ''F'' that has the same first-order properties as the field of real numbers. Some examples are the field of real numbers, the field of real algebraic numbers, and the field of hyperreal numbers. Def ...
* Artin–Schreier theory * Schreier's subgroup lemma *
Schreier–Sims algorithm The Schreier–Sims algorithm is an algorithm in computational group theory, named after the mathematicians Otto Schreier and Charles Sims. This algorithm can find the order of a finite permutation group, test membership (is a given permutation ...
* Schreier coset graph * Schreier conjecture *
Schreier domain In abstract algebra, a Schreier domain, named after Otto Schreier, is an integrally closed domain where every nonzero element is primal; ''i.e.'', whenever ''x'' divides ''yz'', ''x'' can be written as ''x'' = ''x''1 ''x''2 so that ''x''1 divides ...


References


External links

* * {{DEFAULTSORT:Schreier, Otto 1901 births 1929 deaths 20th-century Austrian mathematicians Austrian Jews Group theorists Combinatorial group theory