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Otto Schreier
Otto Schreier (3 March 1901 in Vienna, Austria – 2 June 1929 in Hamburg, Germany) was a Jewish-Austrian mathematician who made major contributions in combinatorial group theory and in the topology of Lie groups. Life His parents were the architect :de:Theodor_Schreier, 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 (mathematician), Hans Hahn, Kurt Reidemeister, Leopold Vietoris, and Josef Lense. In 1923 he obtained his doctorate, under the supervision of Philipp Furtwängler, entitled ''On the expansion of groups (Über die Erweiterung von Gruppen)''. In 1926 he completed his habilitation 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 h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Józef Schreier
Józef Schreier (; 18 February 1909, Drohobycz, Austria-Hungary – April 1943, Drohobycz, Occupied Poland) was a Polish mathematician of Jewish origin, known for his work in functional analysis, group theory and combinatorics. He was a member of the Lwów School of Mathematics and a victim of the Holocaust. Józef Schreier was born on 18 February 1909 in Drohobycz. His father was a rabbi and doctor of philosophy. His cousin was the musician Alfred Schreyer. From 1927-31 he studied at the Jan Kazimierz University in Lwów. In his first published paper, he defined what later came to be known as Schreier sets in order to show that not all Banach spaces possess the weak Banach-Saks property, disproving a conjecture of Stefan Banach and Stanisław Saks. Schreier sets were later discovered independently by researchers in Ramsey theory. Schreier completed his master's degree ''On tournament elimination systems'' in 1932 under the direction of Hugo Steinhaus. Schreier correctly c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Josef Lense
Josef Lense (28 October 1890 in Vienna – 28 December 1985 in Munich) was an Austrian physicist. In 1914 Lense obtained his doctorate under Samuel Oppenheim. From 1927-28 he was Professor ordinarius and from 1928–1946 Professor extraordinarius for applied mathematics at the Technical University of Munich. From 1946 until 1961 he was director of the mathematical institute of the same university. Lense, together with Hans Thirring Hans Thirring (23 March 1888 – 22 March 1976) was an Austrian theoretical physicist, professor, and father of the physicist Walter Thirring. He won the Haitinger Prize of the Austrian Academy of Sciences in 1920. Together with the mathematic ..., is known as one of the two discoverers of the Lense-Thirring effect. Publications *Lense, J. and Thirring, H. Über den Einfluss der Eigenrotation der Zentralkörper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie. ''Physikalische Zeitschrift'' 19 156-63 (19 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Emanuel Sperner
Emanuel Sperner (9 December 1905 – 31 January 1980) was a German mathematician, best known for two theorems. He was born in Waltdorf (near Neiße, Upper Silesia, now Nysa, Poland), and died in Sulzburg-Laufen, West Germany. He was a student at Carolinum in Nysa and then Hamburg University where his advisor was Wilhelm Blaschke. He was appointed Professor in Königsberg in 1934, and subsequently held posts in a number of universities until 1974. Sperner's theorem, from 1928, says that the size of an antichain in the power set of an ''n''-set (a Sperner family) is at most the middle binomial coefficient(s). It has several proofs and numerous generalizations, including the Sperner property of a partially ordered set. Sperner's lemma, from 1928, states that every Sperner coloring of a triangulation of an ''n''-dimensional simplex contains a cell colored with a complete set of colors. It was proven by Sperner to provide an alternate proof of a theorem of Lebesgue charact ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Classification Theorem
In mathematics, a classification theorem answers the classification problem: "What are the objects of a given type, up to some equivalence?". It gives a non-redundant enumeration: each object is equivalent to exactly one class. A few issues related to classification are the following. *The equivalence problem is "given two objects, determine if they are equivalent". *A complete set of invariants, together with which invariants are realizable, solves the classification problem, and is often a step in solving it. (A combination of invariant values is realizable if there in fact exists an object whose invariants take on the specified set of values) *A (together with which invariants are realizable) solves both the classification problem and the equivalence problem. * A canonical form solves the classification problem, and is more data: it not only classifies every class, but provides a distinguished (canonical) element of each class. There exist many classification theorems in mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Schreier Conjecture
In finite group theory, the Schreier conjecture asserts that the outer automorphism group 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 Proof most often refers to: * Proof (truth), argument or sufficient evidence for the truth of a proposition * Alcohol proof, a measure of an alcoholic drink's strength Proof may also refer to: Mathematics and formal logic * Formal proof, a co ... is known. References *. Theorems about finite groups Conjectures that have been proved {{Abstract-algebra-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Real Closed Field
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. Definition A real closed field is a field ''F'' in which any of the following equivalent conditions is true: #''F'' is elementarily equivalent to the real numbers. In other words, it has the same first-order properties as the reals: any sentence in the first-order language of fields is true in ''F'' if and only if it is true in the reals. #There is a total order on ''F'' making it an ordered field such that, in this ordering, every positive element of ''F'' has a square root in ''F'' and any polynomial of odd degree with coefficients in ''F'' has at least one root in ''F''. #''F'' is a formally real field such that every polynomial of odd degree with coefficients in ''F'' has at least one root in ''F'', and for every element ''a'' o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Artin-Schreier Theorem
In mathematics, a real closed field is a field (mathematics), field F that has the same first-order logic, 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. Definition A real closed field is a field ''F'' in which any of the following equivalent conditions is true: #''F'' is elementarily equivalent to the real numbers. In other words, it has the same first-order properties as the reals: any sentence (mathematical logic), sentence in the first-order language of fields is true in ''F'' if and only if it is true in the reals. #There is a total order on ''F'' making it an ordered field such that, in this ordering, every positive element of ''F'' has a Square root#In integral domains, including fields, square root in ''F'' and any polynomial of parity (mathematics), odd degree of a polynomial, degree with coefficients in ''F'' has at least one Root of a function, r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Emil Artin
Emil Artin (; March 3, 1898 – December 20, 1962) was an Austrians, Austrian mathematician of Armenians, 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 largely to class field theory and a new construction of L-functions. He also contributed to the pure theories of rings, groups and fields. Along with Emmy Noether, he is considered the founder of modern abstract algebra. Early life and education Parents Emil Artin was born in Vienna to parents Emma Maria, née Laura (stage name Clarus), a soubrette on the operetta stages of Austria and Germany, and Emil Hadochadus Maria Artin, Austrian-born of mixed Austrians, Austrian and Armenian people, Armenian descent. His Armenian last name was Artinian which was shortened to Artin. Several documents, including Emil's birth certificate, list the father's occupation as "opera singer" though others list it as "art dealer." It see ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Composition Series
In abstract algebra, a composition series provides a way to break up an algebraic structure, such as a group or a module, into simple pieces. The need for considering composition series in the context of modules arises from the fact that many naturally occurring modules are not semisimple, hence cannot be decomposed into a direct sum of simple modules. A composition series of a module ''M'' is a finite increasing filtration of ''M'' by submodules such that the successive quotients are simple and serves as a replacement of the direct sum decomposition of ''M'' into its simple constituents. A composition series may not exist, and when it does, it need not be unique. Nevertheless, a group of results known under the general name Jordan–Hölder theorem asserts that whenever composition series exist, the ''isomorphism classes'' of simple pieces (although, perhaps, not their ''location'' in the composition series in question) and their multiplicities are uniquely determined. Compos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 group presentation consisting of a set of generators with no relations. That is, every element is a product of some sequence of generators and their inverses, but these elements do not obey any equations except those trivially following from = 1. The elements of a free group may be described as all possible reduced words, those strings of generators and their inverses in which no generator is adjacent to its own inverse. Two reduced words may be multiplied by concatenating them and then removing any generator-inverse pairs that result from the concatenation. The Nielsen–Schreier theorem states that if ''H'' is a subgroup of a free group ''G'', then ''H'' is itself isomorphic to a free group. That is, there exists a set ''S'' of element ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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. Dehn's early life and career took place in Germany. However, he was forced to retire in 1935 and eventually fled Germany in 1939 and emigrated to the United States.The story of his travel in 1940 from Norway via Stockholm, Moscow, trans-Siberian train, Vladivostok, Japan to San Francisco is described in Dehn was a student of David Hilbert, and in his habilitation in 1900 Dehn resolved Hilbert's third problem, making him the first to resolve one of Hilbert's problems, Hilbert's well-known 23 problems. Dehn's doctoral students include Ott-Heinrich Keller, Ruth Moufang, and Wilhelm Magnus; he also mentored mathematician Peter Nemenyi and the artists Dorothea Rockburne and Ruth Asawa. Biography Dehn was born to a family of Jewish origin in Hamburg, Imperial Germany. He studied the foundations of geometry with David Hilbert, Hil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 camps. Its conditions were deliberately engineered to hasten the death of its prisoners, and the ghetto also served a propaganda role. Unlike other ghettos, the use of slavery was not economically significant. The ghetto was established by the transportation of Czech Jews in November 1941. The first German and Austrian Jews arrived in June 1942; Dutch and Danish Jews came in 1943, and prisoners of a wide variety of nationalities were sent to Theresienstadt in the last months of the war. About 33,000 people died at Theresienstadt, mostly from malnutrition and disease. More than 88,000 people were held there for months or years before being deported to extermination camps and other killing sites; the role of the Jewish Council ('' Juden ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
