If G is a finitely generated group with exponent n, is G necessarily finite?
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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 that differ in the additional conditions imposed on the orders of the group elements (see bounded and restricted below). Some of these variants are still open questions.
The Burnsideproblem asks whether a finitely generated group in which every element has finite order must necessarily be a finite group. It was posed by...
University and was known for his work in group theory, especially on the Burnsideproblem. Adian was born near Elizavetpol. He grew up there in an Armenian family...
for instance by Tarski monster groups constructed by Olshanskii. Burnside'sproblem is a classical question that deals with the relationship between periodic...
sometimes confused with the Irish mathematician William S. Burnside (1839–1920). William Burnside (2 July 1852 – 21 August 1927) was an English mathematician...
Look up Burnside or burnside in Wiktionary, the free dictionary. Burnside may refer to: Burnside Ridges, Oates Land City of Burnside, a local government...
number of algorithmically insoluble problems, most notably the word problem for groups; and the classical Burnsideproblem. See (Chandler & Magnus 1982) for...
work on combinatorial problems in nonassociative algebra and group theory, including his solution of the restricted Burnsideproblem. He was awarded a Fields...
Sergei Adian, known for his work in group theory, especially on the Burnsideproblem Aleksandr Aleksandrov, developer of CAT(k) space and Alexandrov's uniqueness...
day tended to leak hot gas when fired, but Burnside's design eliminated this problem. In 1857, the Burnside carbine won a competition at West Point against...
open problems. As in other areas of mathematics, such problems are often made public at professional conferences and meetings. Many of the problems posed...
the Burnsideproblem in group theory. Kurosh asked whether there can be a finitely-generated infinite-dimensional algebraic algebra (the problem being...
Shafarevich at the Steklov Institute of Mathematics with a thesis on the Burnsideproblem. He became a faculty member at Moscow State University in 1963. Kostrikin...
The Burnside Fountain is a non-functioning drinking fountain at the southeast corner of Worcester Common in Worcester, Massachusetts. It consists of two...
Sylvia; Gruber, David (21 August 2006). "Manifold Destiny: A legendary problem and the battle over who solved it". The New Yorker. Archived from the original...
of Serge Lang's map allowed a revolution in algebraic groups. The Burnsideproblem had tremendous progress, with better counterexamples constructed in...
Cannonito, F.B.; Lyndon, Roger C. (1973). Word problems : decision problems and the Burnsideproblem in group theory. Studies in logic and the foundations...
and Naimark's problem Pyotr Novikov, solved the word problem for groups and Burnside'sproblem Sergei Novikov, worked on algebraic topology and soliton...
constitutes Golod and Shafarevich's negative solution of the generalized Burnsideproblem in 1964; later, other explicit examples of infinite finitely generated...
his work on combinatorial problems in group theory: the word problem for groups, and his progress in the Burnsideproblem. In 1955, he proved the Novikov–Boone...
word problem solvable by Dehn's algorithm. Small cancellation methods are also used for constructing Tarski monsters, and for solutions of Burnside's problem...
three. The series was produced in Leeds by Yorkshire Television. Neil Burnside (Roy Marsden) is director of operations (D/Ops) in Britain's Secret Intelligence...
Exponentiating by squaring Knapsack problem Shor's algorithm Standard Model Symmetry in physics Burnside'sproblem Classification of finite simple groups...
Neumann, The isomorphism problem for algebraically closed groups, in: Word Problems, Decision Problems, and the BurnsideProblem in Group Theory, Amsterdam-London...
The City of Burnside is a local government area in the South Australian city of Adelaide stretching from the Adelaide Parklands into the Adelaide foothills...
counterexamples to conjectures in group theory, most importantly to Burnside'sproblem and the von Neumann conjecture. Let p {\displaystyle p} be a fixed...
Progress on traditional combinatorial group theory topics, such as the Burnsideproblem, the study of Coxeter groups and Artin groups, and so on (the methods...
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