THE RESTRICTED BURNSIDE PROBLEM

1991 ◽  
Vol 23 (2) ◽  
pp. 201-203
Author(s):  
J. Wiegold
Keyword(s):  
Burnside Problem ◽  
Restricted Burnside Problem

scholarly journals The restricted Burnside problem for Moufang loops

2021 ◽  
pp. 1-11
Author(s):  
ALEXANDER GRISHKOV ◽  
LIUDMILA SABININA ◽  
EFIM ZELMANOV
Keyword(s):  
Prime Number ◽  
Burnside Problem ◽  
Moufang Loops ◽  
Restricted Burnside Problem ◽  
Positive Integers

Abstract We prove that for positive integers $m \geq 1, n \geq 1$ and a prime number $p \neq 2,3$ there are finitely many finite m-generated Moufang loops of exponent $p^n$ .

scholarly journals Bounds in the restricted Burnside problem

1999 ◽  
Vol 67 (2) ◽  
pp. 261-271 ◽  
Author(s):  
Michael Vaughan-Lee ◽  
E. I. Zel'manov
Keyword(s):  
Burnside Problem ◽  
Current State ◽  
Restricted Burnside Problem

AbstractWe survey the current state of knowledge of bounds in the restricted Burnside problem. We make two conjectures which are related to the theory of PI-algebras.

The Algebra of Dimension-Linking Operators

1965 ◽  
Vol 8 (2) ◽  
pp. 203-222 ◽  
Author(s):  
R. H. Bruck
Keyword(s):  
Group Theory ◽  
Special Reference ◽  
Mathematical Society ◽  
Summer Institute ◽  
Burnside Problem ◽  
The Third ◽  
Australian Mathematical Society ◽  
Suitable Definition ◽  
Definition Of ◽  
Restricted Burnside Problem

In the course of preparing a book on group theory [1] with special reference to the Restricted Burnside Problem and allied problems I stumbled upon the concept of a dimension-linking operator. Later, when I lectured to the Third Summer Institute of the Australian Mathematical Society [2], G. E. Wall raised the question whether the dimension-linking operators could be made into a ring by introduction of a suitable definition of multiplication. The answer was easily found to be affirmative; the result wasthat the theory of dimen sion-linking operators became exceedingly simple.

scholarly journals Semiregular elements in cubic vertex-transitive graphs and the restricted Burnside problem

2014 ◽  
Vol 157 (1) ◽  
pp. 45-61
Author(s):  
PABLO SPIGA
Keyword(s):  
Automorphism Group ◽  
Positive Solution ◽  
Cayley Graph ◽  
Burnside Problem ◽  
Transitive Graph ◽  
Vertex Transitive ◽  
Vertex Transitive Graphs ◽  
Restricted Burnside Problem ◽  
Vertex Transitive Graph ◽  
Transitive Graphs

AbstractIn this paper, we prove that the maximal order of a semiregular element in the automorphism group of a cubic vertex-transitive graph Γ does not tend to infinity as the number of vertices of Γ tends to infinity. This gives a solution (in the negative) to a conjecture of Peter Cameron, John Sheehan and the author [4, conjecture 2].However, with an application of the positive solution of the restricted Burnside problem, we show that this conjecture holds true when Γ is either a Cayley graph or an arc-transitive graph.

scholarly journals A Theorem in Semigroups Inspired by the Restricted Burnside Problem

2000 ◽  
Vol 226 (1) ◽  
pp. 621-628 ◽  
Author(s):  
S.P. Strunkov ◽  
K.P. Shum
Keyword(s):  
Burnside Problem ◽  
Restricted Burnside Problem

NILPOTENT LINEAR SEMIGROUPS

2006 ◽  
Vol 16 (01) ◽  
pp. 141-160 ◽  
Author(s):  
ERIC JESPERS ◽  
DAVID RILEY
Keyword(s):  
Finite Group ◽  
Lie Algebra ◽  
Associative Algebra ◽  
Burnside Problem ◽  
Finitely Generated ◽  
Residually Finite ◽  
Residually Finite Group ◽  
Adjoint Semigroup ◽  
Restricted Burnside Problem ◽  
Global And Local

We characterize the structure of linear semigroups satisfying certain global and local nilpotence conditions and deduce various Engel-type results. For example, using a form of Zel'manov's solution of the restricted Burnside problem we are able to show that a finitely generated residually finite group is nilpotent if and only if it satisfies a certain 4-generator property of semigroups we call WMN. Methods of linear semigroups then allow us to prove that a linear semigroup is Mal'cev nilpotent precisely when it satisfies WMN. As an application, we show that a finitely generated associative algebra is nilpotent when viewed as a Lie algebra if and only if its adjoint semigroup is WMN.

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