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Paul E. Schupp
Paul Eugene Schupp (born March 12, 1937, died January 24, 2022) was a professor emeritus of mathematics at the University of Illinois at Urbana Champaign. He is known for his contributions to geometric group theory, computational complexity and the theory of computability. He received his Ph.D. from the University of Michigan in 1966 under the direction of Roger Lyndon. Together with Roger Lyndon he is the coauthor of the book "Combinatorial Group Theory" which provided a comprehensive account of the subject of Combinatorial Group Theory, starting with the work of Dehn in the 1910s and to late 1970s and remains a modern standard for the subject of small cancellation theory. Starting 1980's he worked on problems that explored the connections between Group theory and Computer Science and Complexity Theory. Together with David Muller he proved that a finitely generated group ''G'' has context-free word problem if and only if ''G'' is virtually free, which is now known as Mul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cleveland, Ohio
Cleveland ( ), officially the City of Cleveland, is a city in the U.S. state of Ohio and the county seat of Cuyahoga County. Located in the northeastern part of the state, it is situated along the southern shore of Lake Erie, across the U.S. maritime border with Canada, northeast of Cincinnati, northeast of Columbus, and approximately west of Pennsylvania. The largest city on Lake Erie and one of the major cities of the Great Lakes region, Cleveland ranks as the 54th-largest city in the U.S. with a 2020 population of 372,624. The city anchors both the Greater Cleveland metropolitan statistical area (MSA) and the larger Cleveland–Akron–Canton combined statistical area (CSA). The CSA is the most populous in Ohio and the 17th largest in the country, with a population of 3.63 million in 2020, while the MSA ranks as 34th largest at 2.09 million. Cleveland was founded in 1796 near the mouth of the Cuyahoga River by General Moses Cleaveland, after whom the city was named ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Small Cancellation Theory
In the mathematical subject of group theory, small cancellation theory studies groups given by group presentations satisfying small cancellation conditions, that is where defining relations have "small overlaps" with each other. Small cancellation conditions imply algebraic, geometric and algorithmic properties of the group. Finitely presented groups satisfying sufficiently strong small cancellation conditions are word hyperbolic and have word problem solvable by Dehn's algorithm. Small cancellation methods are also used for constructing Tarski monsters, and for solutions of Burnside's problem. History Some ideas underlying the small cancellation theory go back to the work of Max Dehn in the 1910s. Dehn proved that fundamental groups of closed orientable surfaces of genus at least two have word problem solvable by what is now called Dehn's algorithm. His proof involved drawing the Cayley graph of such a group in the hyperbolic plane and performing curvature estimates via the Ga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Michigan Alumni
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, the designation is reserved for colleges that have a graduate school. The word ''university'' is derived from the Latin ''universitas magistrorum et scholarium'', which roughly means "community of teachers and scholars". The first universities were created in Europe by Catholic Church monks. The University of Bologna (''Università di Bologna''), founded in 1088, is the first university in the sense of: *Being a high degree-awarding institute. *Having independence from the ecclesiastic schools, although conducted by both clergy and non-clergy. *Using the word ''universitas'' (which was coined at its foundation). *Issuing secular and non-secular degrees: grammar, rhetoric, logic, theology, canon law, notarial law.Hunt Janin: "The university ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stevens Institute Of Technology
Stevens Institute of Technology is a private research university in Hoboken, New Jersey. Founded in 1870, it is one of the oldest technological universities in the United States and was the first college in America solely dedicated to mechanical engineering. The 55-acre campus encompasses Castle Point, the highest point in Hoboken, a campus green and 43 academic, student and administrative buildings. Established through an 1868 bequest from Edwin Augustus Stevens, enrollment at Stevens includes more than 8,000 undergraduate and graduate students representing 47 states and 60 countries throughout Asia, Europe and Latin America. Stevens comprises three schools and one college that deliver technology-based STEM (science, technology, engineering and mathematics) degrees and degrees in business, arts, humanities and social sciences: The Charles V. Schaefer, Jr., School of Engineering and Science, School of Business, School of Systems and Enterprises, and College of Arts and Letters. F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance, due to concerns about competing with the American Journal of Mathematics. The result was the ''Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influential in in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Computer And System Sciences
The ''Journal of Computer and System Sciences'' (JCSS) is a peer-reviewed scientific journal in the field of computer science. ''JCSS'' is published by Elsevier, and it was started in 1967. Many influential scientific articles have been published in ''JCSS''; these include five papers that have won the Gödel Prize. an 2014 Gödel Prize Its managing editor is |
Virtually Free Group
In mathematics, especially in the area of abstract algebra that studies infinite groups, the adverb virtually is used to modify a property so that it need only hold for a subgroup In group theory, a branch of mathematics, given a group ''G'' under a binary operation ∗, a subset ''H'' of ''G'' is called a subgroup of ''G'' if ''H'' also forms a group under the operation ∗. More precisely, ''H'' is a subgroup ... of finite Index of a subgroup, index. Given a property P, the group ''G'' is said to be ''virtually P'' if there is a finite index subgroup H \le G such that ''H'' has property P. Common uses for this would be when P is Abelian group, abelian, Nilpotent group, nilpotent, solvable group, solvable or Free group, free. For example, virtually solvable groups are one of the two alternatives in the Tits alternative, while Gromov's theorem on groups of polynomial growth, Gromov's theorem states that the finitely generated groups with Growth rate (group theory), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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