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Topic: Restricted Burnside problem

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	Burnside's problem - Wikipedia, the free encyclopedia
		One of the oldest open problems in group theory was first posed by William Burnside in a paper published in 1902.
		Some variations of the problem which were also stated in this paper have been resolved; but a full solution to the basic problem is still open as of 2004.
		The restricted Burnside problem was answered in the affirmative in 1991 by Efim Zelmanov, for which he was awarded the Fields Medal in 1994.
	en.wikipedia.org /wiki/Burnside's_problem (756 words)

	groups (Site not responding. Last check: 2007-10-03)
		Burnside himself showed that B (d,3) is finite.
		The General Burnside problem was shown to have a negative solution by Golod in 1964.
		Restricted Burnside problem, the appearance of Jordan algebras is unprecedented and quite surprising."
	www.math.uiuc.edu /~selvkmrn/groups.html (710 words)

	Burnside's problem
		Some variations of the problem which were also stated in this paper have been resolved; but a full solution to the basic problem is still open as of 2002.
		The restricted Burnside problem (formulated in the 1930s) asks another related question: are there only finitely many finite r-generator groups of exponent n?
		The restricted Burnside problem was answered in the affirmative by Efim Zelmanov[?], for which he was awarded the Fields Medal in 1994.
	www.ebroadcast.com.au /lookup/encyclopedia/bu/Burnside's_problem.html (658 words)

	Search Results for problem*
		In her thesis Definability and decision problems in arithmetic Robinson proved that the arithmetic of rational numbers is undecidable by giving an arithmetical definition of the integers in the rationals.
		Open problems and unresolved difficulties are carefully noted, and the reader is never left in doubt as to whether he is presented with a mathematical theorem or with a conjecture based on physical experience.
		After considering the problem of conformal mapping on the half-plane of finite polygonal regions bounded by straight lines and circular arcs she applied these ideas to the physical problem of the two-dimensional seepage flow of ground water in an earth dam of a particular shape.
	www-gap.dcs.st-and.ac.uk /~history/Search/historysearch.cgi?SUGGESTION=problem*&CONTEXT=1 (18472 words)

	Burnside problem
		Burnside and Schur made early progress on the problems in two papers, which confirmed that the problem would certainly not be straightforward:
		Despite this formulation having been present on the seminar circuit in the 1930's, it was not until 1940 that the first paper, by Grün [J.f.d.
		P Hall and G Higman [p-length of p-soluble groups and reduction theorems for Burnside\'s Problem, Proc.
	www-groups.dcs.st-and.ac.uk /~history/HistTopics/Burnside_problem.html (1011 words)

	Selected publications
		I show that the associated Lie ring of the largest finite 3-generator group of exponent 5 has dimension 2282, and that it is a free Lie algebra in the variety of Lie algebras determined by the multilinear identities satisfied by the associated Lie rings of groups of exponent 5.
		This book aims to give a unified treatment of the restricted Burnside problem using the theory of the multilinear identities which hold in the associated Lie rings of groups of prime-power exponent.
		The proof uses the classification of finite simple groups, together with the Hall-Higman reduction of the restricted Burnside problem to the case of prime-power exponent.
	users.ox.ac.uk /~vlee/selected.htm (925 words)

	2 Groups (Site not responding. Last check: 2007-10-03)
		Problem 1 (General Burnside Problem) Let G be a finitely generated group such that for every element g of G there is a positive integer N
		When G arises as a group of n×n matrices (or more formally when G is a linear group) it was shown by Burnside that the answer is yes (a simple proof is outlined in Appendix A).
		Problem 2 (Ordinary Burnside Problem) Let G be a finitely generated group for which there is a positive integer N such that for every element g we have g
	www.imsc.res.in /~kapil/papers/zelm/node2.html (393 words)

	Zelmanov (print-only)
		Let me explain the background to the restricted Burnside problem, the solution of which was the main reason for the award of the Medal, and also explain how Zelmanov, not a group theorist by training, came to solve one of the most fundamental questions in group theory.
		This problem is known as the General Burnside problem.
		While Lie algebras have long been considered a natural playground in the context of the Restricted Burnside problem, the appearance of Jordan algebras is unprecedented and quite surprising.
	www-history.mcs.st-and.ac.uk /Printonly/Zelmanov.html (1005 words)

	[No title] (Site not responding. Last check: 2007-10-03)
		It was first asked by Burnside in 1902, and so is known as the Burnside Problem.
		One reference for the proof is the chapter on the Burnside Problem in M.
		This is of course a special case of the well-known Burnside Problem.
	www.math.niu.edu /~rusin/known-math/96/burnside.prob (744 words)

	Burnside problem
		Despite this formulation having been present on the seminar circuit in the 1930's, it was not until 1940 that the first paper, by Grün [6], appeared specifically addressing the RBP, and not until 1950 that the term "Restricted Burnside Problem" was coined by Magnus [7].
		Golod and Shafarevich [15] provided a counter-example to the General Burnside Problem -- an infinite, finitely generated, periodic group.
		Zelmanov was awarded a Fields medal for his positive solution of the Restricted Burnside Problem.
	www-groups.dcs.st-and.ac.uk /history/PrintHT/Burnside_problem.html (866 words)

	Abstracts of talks
		A tiling-sequence is a sequence of tilings of a planar or spherical domain where the first tiling is given and the subsequent tilings arise from the first by a well-defined finite subdivision rule.
		The fundamental problem is to determine which tiling-sequences, given combinatorially, can be realized geometrically so that they are (essentially) preserved by the action of a Kleinian group.
		Abstract: I will discuss the problem of estimating the number of nonsingular matrices in the orthogonal group $O^\pm (d,q)$ ($d$ and $q$ even) for which the only fixed vector in the underlying vector space $V$ is the zero vector.
	www.math.unl.edu /~mbrittenham2/ldt/conf/canber96.html (2833 words)

	May 1998 Seminars (Site not responding. Last check: 2007-10-03)
		This problem asks: given any natural numbers d and n, is there a bound on the order of d-generated finite group G of exponent n?
		Zelmanov's approach was to first solve a corresponding Lie ring-theoretic Burnside-Type problem and then to deduce from it the Restricted Burnside Problem for Groups.
		Algorithms for generating a random spanning tree are connected to generation and counting of states in arbitrary Markov chains.
	www.math.gatech.edu /aco/events/old/csem/may98.html (876 words)

	Encyclopedia :: encyclopedia : Rhode Island (Site not responding. Last check: 2007-10-03)
		By 1829, 60% of the state's free white males were ineligible to vote.
		Several attempts had been made to address this problem, but none passed.
		The Republican Party has been restricted to more rural parts of the state, and occasional so-called "good government" reform candidates, who criticize the excesses of Democratic domination.
	www.hallencyclopedia.com /Rhode_Island (1904 words)

	Colloquim
		is false.The corresponding problem for the irrationals is unsolved, but a positive answer is consistent with the usual axioms of set theory.
		Except for the consistency proof (the details of which will be omitted) the methods are reasonably accessible: classical topology of the real line and elementary consequences of the definition of ''elementary submodel''.
		is a new phenomenon in the classification problem
	www.math.uwo.ca /~milnes/coll0102.htm (1479 words)

	[No title]
		You have stated the so-called Burnside problem: is the group B(r, n) finite?
		Zelmanov got the Fields medal for this result, which gives a positive solution to the so-called restricted Burnside problem.
		B(2,5) is the smallest unknown case, and is one of the most challenging open problems in group theory at present.
	www.math.niu.edu /~rusin/known-math/99/burnside (987 words)

	Group Theory (Site not responding. Last check: 2007-10-03)
		At present we have the culmination of a three directional attack on the Burnside problems.
		The first consists of the geometric methods of Ol'Shanskii in producing finitely generated groups of finite exponent that are infinite (a vast improvement of Adian's construction which is one of the technically most difficult piece of work of over 300 pages!).
		The second is the positive solution of the restricted Burnside Problem for residually finite groups by Zelmanov, and the third is the p-adic analytic methods in dealing with questions of linearity of residually finite groups by Alex Lubotzky and Avinoam Mann.
	www.pims.math.ca /science/2000/algebra2000/GroupThm.html (304 words)

	Research interests
		For many years most of my research was centred on the restricted Burnside problem: "Given positive integers m and n, is there a bound on the orders of finite m-generator groups of exponent n?" This question was answered in the affirmative by Efim Zel'manov in 1991.
		#Upper bounds in the restricted Burnside problem, J. Algebra 162 (1993), 107-145, and
		#Upper bounds in the restricted Burnside problem II, International J. Algebra and Computation 6 (1996), 735-744.) And I have used computers to obtain information about groups of exponent 4, 5 and 7.
	users.ox.ac.uk /~vlee/research.htm (545 words)

	Citebase - Burnside obstructions to the Montesinos-Nakanishi 3-move conjecture (Site not responding. Last check: 2007-10-03)
		We define the n-th Burnside group of a link and use the 3rd Burnside group to answer Nakanishi's question; ie, we show that some links cannot be reduced to trivial links by 3-moves.
		This is a list of open problems on invariants of knots and 3-manifolds with expositions of their history, background, significance, or importance.
		This list was made by editing open problems given in problem sessions in the workshop and seminars on `Invariants of Knots and 3-Manifolds' held at Kyo...
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:math/0205040 (1145 words)

	On Zel'manov's solution of the restricted Burnside problem (ResearchIndex) (Site not responding. Last check: 2007-10-03)
		4 The restricted Burnside problem (context) - Vaughan-Lee - 1993
		3 Upper bounds in the restricted Burnside problem (context) - Vaughan-Lee, Zel'manov - 1993
		1 Upper bounds in the restricted Burnside problem II (context) - Vaughan-Lee, Zel'manov - 1996
	citeseer.ist.psu.edu /361039.html (269 words)

	► » groups (Site not responding. Last check: 2007-10-03)
		problem, and solved in the negative by Novikov and Adjan in 1968:
		any of the known examples in the Burnside problem.
		positive solution to the restricted Burnside problem, G is indeed
	www.science-chat.org /groups-5328605.html (504 words)

	Higman biography
		It is this paper which introduced many important ideas but the most significant result was a reduction theorem for the restricted Burnside problem which essentially reduced the problem to looking only at groups of prime power exponent.
		This result plays a vital part in Zelmanov's positive solution to the restricted Burnside problem in the early 1990s.
		Together with Bill Boone, Higman worked on the word problem and together they wrote two papers on the algebraic structure of groups with soluble word problem and with soluble order problem.
	www-history.mcs.st-and.ac.uk /Biographies/Higman.html (1322 words)

	Unexpected connections between Burnside groups and knot theory -- Dabkowski and Przytycki 101 (50): 17357 -- ... (Site not responding. Last check: 2007-10-03)
		Unexpected connections between Burnside groups and knot theory -- Dabkowski and Przytycki 101 (50): 17357 -- Proceedings of the National Academy of Sciences
		as predicted by Burnside (8) and verified by Tobin (19).
		Kirby, R. (1997) in Problems in Low-Dimensional Topology: Geometric Topology, Proceedings of the Georgia International Topology Conference 1993, Studies in Advanced Mathematics, ed.
	intl.pnas.org /cgi/content/full/101/50/17357 (1577 words)

	Chronology for 1990 to 2000
		Unlike "Hilbert's problems" from 100 years earlier, these were given by a team of 30 leading mathematicians of whom eight were
		A prize of seven million dollars is put up for the solution of seven famous mathematical problems.
		Called the Millennium Prize Problems they are: P versus NP; The "Hodge Conjecture"; The
	www-gap.dcs.st-and.ac.uk /~history/Chronology/1990_2000.html (282 words)

	Lecture Series History (Site not responding. Last check: 2007-10-03)
		On April 5, 1996, he spoke again on progress in an area close to the classical Burnside problem in group theory.
		On November 5, 1993, Professor Daniel Tataru, Northwestern University presented his solution of a longstanding problem in the theory of partial differential equations about the sharp uniqueness domain in the (time-like) Cauchy problem for hyperbolic equations with time-independent coefficients.
		Unifying methods of top analysts (Hörmander, Robbiano), he used the "heat equation" transform to show that uniqueness is the same as in the classical Holmgren-John Theorem for equation, with analytic coefficients.
	www.math.wichita.edu /events/lecture-series-history (489 words)

	zelmanov
		By the 1930s no real progress had been made on either of these problems and the Restricted Burnside problem was formulated (and so named by
		This is equivalent to saying that a positive solution to the Restricted Burnside problem would show that there are only finitely many finite
		At the Groups-St Andrews conference at Galway, Ireland in 1993, of which I [EFR] was a joint organiser, Zelmanov was one of the main speakers and he gave a series of five lectures on
	www.koyli.com /zelmanov.htm (920 words)

	Rhode_Island
		The Democratic Party represented a coalition of labor unions, working class immigrants, intellectuals, college students, and the rising ethnic middle class.
		The Republican Party has been restricted to the rural and suburban parts of the state, and occasional "good government" reform candidates, who criticize the state's high taxes and the excesses of Democratic domination.
		Cranston Mayor Stephen Laffey, Governor Donald Carcieri of East Greenwich, and former Mayor Vincent A. "Buddy" Cianci of Providence ran as Republican reform candidates.
	www.brainyencyclopedia.com /encyclopedia/r/rh/rhode_island.html (3243 words)

	[No title] (Site not responding. Last check: 2007-10-03)
		The question of the possibility of an unending game of chess leads to the problem of constructing and unending sequence of symbols form a given finite set so that the infinite sequence does not contain a block of the form EEe, where E is itself a block and e is the first symbol in E.
		A.Cobham, "On the Hartmanis-Stearns problem for a class of tag machines", IEEE Conference Record of the 1968 Ninth Annual Symposium on Switching and Automata Theory, Schenectady (1968), 51-60.
		We consider here the problem of determining the set of all sequences of two symbols with the property of not containing a block of the form BBb when b is the initial element of B and show that this set is precisely the collection of sequences constituting the Morse minimal set.
	io.uwinnipeg.ca /~currie/Students/mthpap.html (9379 words)

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