An attack on the restricted burnside problem for groups of exponent 8 on 2 genrators

1973 ◽  
pp. 140-147
Author(s):  
Ricardo B. Quintana
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 $p^n$ .

THE RESTRICTED BURNSIDE PROBLEM

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

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.

The Restricted Burnside Problem

1985 ◽  
Vol 17 (2) ◽  
pp. 113-133 ◽  
Author(s):  
M. R. Vaughan-Lee
Keyword(s):  
Burnside Problem ◽  
Restricted Burnside Problem

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
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