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Koichiro Harada (Violinist)
is a Japanese mathematician working on finite group theory. The Institute for Advanced Study was Harada's first position in the United States in 1968. He graduated from University of Tokyo in 1972. Rutgers University was the scene from 1969 to 73 of his collaboration with Daniel Gorenstein on the classification challenge in finite groups. In 1971 he first taught at Ohio State University, and in 1973 he was a visitor at Cambridge University where the Harada-Norton group was discovered. The Gorenstein–Harada theorem classifies finite simple groups of sectional 2-rank at most 4. In 1996 Ohio State held a Special Research Quarter on the Monster group and Lie algebras with ''Proceedings'' edited by Joseph Ferrar and Harada. In 2000 Mathematical Society of Japan awarded Harada the Algebra Prize. After the classification of finite simple groups was announced, Harada proposed the following challenges to group theorists:Yasuhiko Tanaka (2003Review: "Achievements and problems in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simple Group
SIMPLE Group Limited is a conglomeration of separately run companies that each has its core area in International Consulting. The core business areas are Legal Services, Fiduciary Activities, Banking Intermediation and Corporate Service. The date of incorporation is listed as 1999 by Companies House of Gibraltar, who class it as a holding company; however it is understood that SIMPLE Group's business and trading activities date to the second part of the 90s, probably as an incorporated body. SIMPLE Group Limited is a conglomerate that cultivate secrecy, they are not listed on any Stock Exchange and the group is owned by a complicated series of offshore trust An offshore trust is a conventional trust that is formed under the laws of an offshore jurisdiction. Generally offshore trusts are similar in nature and effect to their onshore counterparts; they involve a settlor transferring (or 'settling') a ...s. The Sunday Times stated that SIMPLE Group's interests could be eval ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century Japanese Mathematicians
The 1st century was the century spanning AD 1 ( I) through AD 100 ( C) according to the Julian calendar. It is often written as the or to distinguish it from the 1st century BC (or BCE) which preceded it. The 1st century is considered part of the Classical era, epoch, or historical period. The 1st century also saw the appearance of Christianity. During this period, Europe, North Africa and the Near East fell under increasing domination by the Roman Empire, which continued expanding, most notably conquering Britain under the emperor Claudius (AD 43). The reforms introduced by Augustus during his long reign stabilized the empire after the turmoil of the previous century's civil wars. Later in the century the Julio-Claudian dynasty, which had been founded by Augustus, came to an end with the suicide of Nero in AD 68. There followed the famous Year of Four Emperors, a brief period of civil war and instability, which was finally brought to an end by Vespasian, ninth Roman emperor, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
European Mathematical Society
The European Mathematical Society (EMS) is a European organization dedicated to the development of mathematics in Europe. Its members are different mathematical societies in Europe, academic institutions and individual mathematicians. The current president is Volker Mehrmann, professor at the Institute for Mathematics at the Technical University of Berlin. Goals The Society seeks to serve all kinds of mathematicians in universities, research institutes and other forms of higher education. Its aims are to #Promote mathematical research, both pure and applied, #Assist and advise on problems of mathematical education, #Concern itself with the broader relations of mathematics to society, #Foster interaction between mathematicians of different countries, #Establish a sense of identity amongst European mathematicians, #Represent the mathematical community in supra-national institutions. The EMS is itself an Affiliate Member of the International Mathematical Union and an Associate Membe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Algebra
''Journal of Algebra'' (ISSN 0021-8693) is an international mathematical research journal in algebra. An imprint of Academic Press, it is published by Elsevier. ''Journal of Algebra'' was founded by Graham Higman, who was its editor from 1964 to 1984. From 1985 until 2000, Walter Feit served as its editor-in-chief. In 2004, ''Journal of Algebra'' announced (vol. 276, no. 1 and 2) the creation of a new section on computational algebra, with a separate editorial board. The first issue completely devoted to computational algebra was vol. 292, no. 1 (October 2005). The Editor-in-Chief of the ''Journal of Algebra'' is Michel Broué, Université Paris Diderot, and Gerhard Hiß, Rheinisch-Westfälische Technische Hochschule Aachen ( RWTH) is Editor of the computational algebra section. See also *Susan Montgomery M. Susan Montgomery (born 2 April 1943 in Lansing, MI) is a distinguished American mathematician whose current research interests concern noncommutative algebras: in parti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Memoirs Of The American Mathematical Society
''Memoirs of the American Mathematical Society'' is a mathematical journal published in six volumes per year, totalling approximately 33 individually bound numbers, by the American Mathematical Society. It is intended to carry papers on new mathematical research between 80 and 200 pages in length. Usually, a bound number consists of a single paper, i.e., it is a monograph. The journal is indexed by Mathematical Reviews, Zentralblatt MATH, Science Citation Index, Research Alert, CompuMath Citation Index, and Current Contents. Other journals from the AMS * ''Bulletin of the American Mathematical Society'' * ''Journal of the American Mathematical Society'' * ''Notices of the American Mathematical Society ''Notices of the American Mathematical Society'' is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue. The first volume appeared in 1953. Each issue of the magazine since ...'' * ''Proceedings of the Ame ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Restricted Burnside Problem
The Burnside problem asks whether a finitely generated group in which every element has finite order must necessarily be a finite group. It was posed by William Burnside in 1902, making it one of the oldest questions in group theory and was influential in the development of combinatorial group theory. It is known to have a negative answer in general, as Evgeny Golod and Igor Shafarevich provided a counter-example in 1964. The problem has many refinements and variants (see bounded and restricted below) that differ in the additional conditions imposed on the orders of the group elements, some of which are still open questions. Brief history Initial work pointed towards the affirmative answer. For example, if a group ''G'' is finitely generated and the order of each element of ''G'' is a divisor of 4, then ''G'' is finite. Moreover, A. I. Kostrikin was able to prove in 1958 that among the finite groups with a given number of generators and a given prime exponent, there exists a l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sylow 2-subgroup
In mathematics, specifically in the field of finite group theory, the Sylow theorems are a collection of theorems named after the Norwegian mathematician Peter Ludwig Sylow that give detailed information about the number of subgroups of fixed order that a given finite group contains. The Sylow theorems form a fundamental part of finite group theory and have very important applications in the classification of finite simple groups. For a prime number p, a Sylow ''p''-subgroup (sometimes ''p''-Sylow subgroup) of a group G is a maximal p-subgroup of G, i.e., a subgroup of G that is a ''p''-group (meaning its cardinality is a power of p, or equivalently, the order of every group element is a power of p) that is not a proper subgroup of any other p-subgroup of G. The set of all Sylow p-subgroups for a given prime p is sometimes written \text_p(G). The Sylow theorems assert a partial converse to Lagrange's theorem. Lagrange's theorem states that for any finite group G the order ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
P-group
In mathematics, specifically group theory, given a prime number ''p'', a ''p''-group is a group in which the order of every element is a power of ''p''. That is, for each element ''g'' of a ''p''-group ''G'', there exists a nonnegative integer ''n'' such that the product of ''pn'' copies of ''g'', and not fewer, is equal to the identity element. The orders of different elements may be different powers of ''p''. Abelian ''p''-groups are also called ''p''-primary or simply primary. A finite group is a ''p''-group if and only if its order (the number of its elements) is a power of ''p''. Given a finite group ''G'', the Sylow theorems guarantee the existence of a subgroup of ''G'' of order ''pn'' for every prime power ''pn'' that divides the order of ''G''. Every finite ''p''-group is nilpotent. The remainder of this article deals with finite ''p''-groups. For an example of an infinite abelian ''p''-group, see Prüfer group, and for an example of an infinite simple ''p''-grou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modular Representation
Modular representation theory is a branch of mathematics, and is the part of representation theory that studies linear representations of finite groups over a field ''K'' of positive characteristic ''p'', necessarily a prime number. As well as having applications to group theory, modular representations arise naturally in other branches of mathematics, such as algebraic geometry, coding theory, combinatorics and number theory. Within finite group theory, character-theoretic results proved by Richard Brauer using modular representation theory played an important role in early progress towards the classification of finite simple groups, especially for simple groups whose characterization was not amenable to purely group-theoretic methods because their Sylow 2-subgroups were too small in an appropriate sense. Also, a general result on embedding of elements of order 2 in finite groups called the Z* theorem, proved by George Glauberman using the theory developed by Brauer, was par ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schur Multiplier
In mathematical group theory, the Schur multiplier or Schur multiplicator is the second homology group H_2(G, \Z) of a group ''G''. It was introduced by in his work on projective representations. Examples and properties The Schur multiplier \operatorname(G) of a finite group ''G'' is a finite abelian group whose exponent divides the order of ''G''. If a Sylow ''p''-subgroup of ''G'' is cyclic for some ''p'', then the order of \operatorname(G) is not divisible by ''p''. In particular, if all Sylow ''p''-subgroups of ''G'' are cyclic, then \operatorname(G) is trivial. For instance, the Schur multiplier of the nonabelian group of order 6 is the trivial group since every Sylow subgroup is cyclic. The Schur multiplier of the elementary abelian group of order 16 is an elementary abelian group of order 64, showing that the multiplier can be strictly larger than the group itself. The Schur multiplier of the quaternion group is trivial, but the Schur multiplier of dihedral 2-groups ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
