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Michael O'Nan
Michael Ernest O'Nan (August 9, 1943, Fort Knox, Kentucky – July 31, 2017, Princeton, New Jersey) was an American mathematician, specializing in group theory. O'Nan received his PhD in 1970 from Princeton University under Daniel Gorenstein with thesis ''A Characterization of the Three-Dimensional Projective Unitary Group over a Finite Field''. He was a professor at Rutgers University. In 1976 he found strong evidence for the existence of a sporadic group, which Charles Sims constructed. The group is now named the O'Nan group after O'Nan. The O'Nan–Scott theorem in group theory is also named after O'Nan, who discovered it independently from Leonard Scott. It describes the maximal subgroup In mathematics, the term maximal subgroup is used to mean slightly different things in different areas of algebra. In group theory, a maximal subgroup ''H'' of a group ''G'' is a proper subgroup, such that no proper subgroup ''K'' contains ''H'' s ...s of the symmetric groups. Selected ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fort Knox, Kentucky
Fort Knox is a United States Army installation in Kentucky, south of Louisville and north of Elizabethtown. It is adjacent to the United States Bullion Depository, which is used to house a large portion of the United States' official gold reserves, and with which it is often conflated. The base covers parts of Bullitt, Hardin and Meade counties. It currently holds the Army Human Resources Center of Excellence, including the Army Human Resources Command. It is named in honor of Henry Knox, Chief of Artillery in the American Revolutionary War and the first United States Secretary of War. For 60 years, Fort Knox was the home of the U.S. Army Armor Center and the U.S. Army Armor School, and was used by both the Army and the Marine Corps to train crews on the American tanks of the day; the last was the M1 Abrams main battle tank. The history of the U.S. Army's Cavalry and Armored forces, and of General George S. Patton's career, is shown at the General George Patton Museum o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximal Subgroup
In mathematics, the term maximal subgroup is used to mean slightly different things in different areas of algebra. In group theory, a maximal subgroup ''H'' of a group ''G'' is a proper subgroup, such that no proper subgroup ''K'' contains ''H'' strictly. In other words, ''H'' is a maximal element of the partially ordered set of subgroups of ''G'' that are not equal to ''G''. Maximal subgroups are of interest because of their direct connection with primitive permutation representations of ''G''. They are also much studied for the purposes of finite group theory: see for example Frattini subgroup, the intersection of the maximal subgroups. In semigroup theory, a maximal subgroup of a semigroup ''S'' is a subgroup (that is, a subsemigroup which forms a group under the semigroup operation) of ''S'' which is not properly contained in another subgroup of ''S''. Notice that, here, there is no requirement that a maximal subgroup be proper, so if ''S'' is in fact a group then its uniq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rutgers University Faculty
This is an enumeration of notable people affiliated with Rutgers University, including graduates of the undergraduate and graduate and professional programs at all three campuses, former students who did not graduate or receive their degree, presidents of the university, current and former professors, as well as members of the board of trustees and board of governors, and coaches affiliated with the university's athletic program. Also included are characters in works of fiction (books, films, television shows, et cetera) who have been mentioned or were depicted as having an affiliation with Rutgers, either as a student, alumnus, or member of the faculty. Some noted alumni and faculty may be also listed in the main Rutgers University article or in some of the affiliated articles. Individuals are sorted by category and alphabetized within each category. Default campus for listings is the New Brunswick campus, the systems' largest campus, with Camden and Newark campus affiliat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Princeton University Alumni
Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the nine colonial colleges chartered before the American Revolution. It is one of the highest-ranked universities in the world. The institution moved to Newark in 1747, and then to the current site nine years later. It officially became a university in 1896 and was subsequently renamed Princeton University. It is a member of the Ivy League. The university is governed by the Trustees of Princeton University and has an endowment of $37.7 billion, the largest endowment per student in the United States. Princeton provides undergraduate and graduate instruction in the humanities, social sciences, natural sciences, and engineering to approximately 8,500 students on its main campus. It offers postgraduate degrees through the Princeton School of Publi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group Theorists
A group is a number of persons or things that are located, gathered, or classed together. Groups of people * Cultural group, a group whose members share the same cultural identity * Ethnic group, a group whose members share the same ethnic identity * Religious group (other), a group whose members share the same religious identity * Social group, a group whose members share the same social identity * Tribal group, a group whose members share the same tribal identity * Organization, an entity that has a collective goal and is linked to an external environment * Peer group, an entity of three or more people with similar age, ability, experience, and interest Social science * In-group and out-group * Primary, secondary, and reference groups * Social group * Collectives Science and technology Mathematics * Group (mathematics), a set together with a binary operation satisfying certain algebraic conditions Chemistry * Functional group, a group of atoms which provide ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1943 Births
Events Below, the events of World War II have the "WWII" prefix. January * January 1 – WWII: The Soviet Union announces that 22 German divisions have been encircled at Stalingrad, with 175,000 killed and 137,650 captured. * January 4 – WWII: Greek-Polish athlete and saboteur Jerzy Iwanow-Szajnowicz is executed by the Germans at Kaisariani. * January 11 ** The United States and United Kingdom revise previously unequal treaty relationships with the Republic of China (1912–1949), Republic of China. ** Italian-American anarchist Carlo Tresca is assassinated in New York City. * January 13 – Anti-Nazi protests in Sofia result in 200 arrests and 36 executions. * January 14 – January 24, 24 – WWII: Casablanca Conference: Franklin D. Roosevelt, President of the United States; Winston Churchill, Prime Minister of the United Kingdom; and Generals Charles de Gaulle and Henri Giraud of the Free French forces meet secretly at the Anfa Hotel in Casablanca, Morocco, to plan the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetric Group
In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions. In particular, the finite symmetric group \mathrm_n defined over a finite set of n symbols consists of the permutations that can be performed on the n symbols. Since there are n! (n factorial) such permutation operations, the order (number of elements) of the symmetric group \mathrm_n is n!. Although symmetric groups can be defined on infinite sets, this article focuses on the finite symmetric groups: their applications, their elements, their conjugacy classes, a finite presentation, their subgroups, their automorphism groups, and their representation theory. For the remainder of this article, "symmetric group" will mean a symmetric group on a finite set. The symmetric group is important to diverse areas of mathematics such as Galois theory, invariant theory, the representatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
O'Nan–Scott Theorem
In mathematics, the O'Nan–Scott theorem is one of the most influential theorems of permutation group theory; the classification of finite simple groups is what makes it so useful. Originally the theorem was about maximal subgroups of the symmetric group. It appeared as an appendix to a paper by Leonard Scott written for The Santa Cruz Conference on Finite Groups in 1979, with a footnote that Michael O'Nan had independently proved the same result. Michael Aschbacher and Scott later gave a corrected version of the statement of the theorem. The theorem states that a maximal subgroup of the symmetric group Sym(Ω), where , Ω, = ''n'', is one of the following: # ''Sk'' × ''Sn−k'' the stabilizer of a ''k''-set (that is, intransitive) # ''Sa '' wr'' Sb'' with ''n'' = ''ab,'' the stabilizer of a partition into ''b'' parts of size ''a'' (that is, imprimitive) #'' primitive'' (that is, preserves no nontrivial partition) and of one of the following types: ::* AGL(''d'',''p'') ::*'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Princeton, New Jersey
Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of which are now defunct. Centrally located within the Raritan Valley region, Princeton is a regional commercial hub for the Central New Jersey region and a commuter town in the New York metropolitan area.New York-Newark, NY-NJ-CT-PA Combined Statistical Area . Accessed December 5, 2020. As of the |
O'Nan Group
In the area of abstract algebra known as group theory, the O'Nan group ''O'N'' or O'Nan–Sims group is a sporadic simple group of order : 2934573111931 : = 460815505920 : ≈ 5. History ''O'Nan'' is one of the 26 sporadic groups and was found by in a study of groups with a Sylow 2-subgroup of " Alperin type", meaning isomorphic to a Sylow 2-Subgroup of a group of type (Z/2''n''Z ×Z/2''n''Z ×Z/2''n''Z).PSL3(F2). For the O'Nan group ''n'' = 2 and the extension does not split. The only other simple group with a Sylow 2-subgroup of Alperin type with ''n'' ≥ 2 is the Higman–Sims group again with ''n'' = 2, but the extension splits. The Schur multiplier has order 3, and its outer automorphism group has order 2. showed that O'Nan cannot be a subquotient of the monster group. Thus it is one of the 6 sporadic groups called the pariahs. Representations showed that its triple cover has two 45-dimensional representations over the field with 7 elements, excha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles Sims (mathematician)
Charles Coffin Sims (April 14, 1937 – October 23, 2017J. J. O'Connor and E. F. Robertson''Charles Sims biography'' MacTutor History of Mathematics archive. Accessed 2018-12-20.) was an American mathematician best known for his work in group theory. Together with Donald G. Higman he discovered the Higman–Sims group, one of the sporadic groups. The permutation group software developed by Sims also led to the proof of existence of the Lyons group (also known as the Lyons–Sims group) and the O'Nan group (also known as the O'Nan–Sims group). Sims was born and raised in Elkhart, Indiana, and received his B.S. from the University of Michigan. He did his graduate studies at Harvard University, where he was a student of John G. Thompson and received his Ph.D. degree in 1963. In his thesis, he enumerated ''p''-groups, giving sharp asymptotic upper and lower bounds. Sims is one of the founders of computational group theory and is the eponym of the Schreier–Sims algorithm. He ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
