scholarly journals Upper Bounds in the Restricted Burnside Problem

1993 ◽  
Vol 162 (1) ◽  
pp. 107-145 ◽  
Author(s):  
M. Vaughanlee ◽  
E.I. Zelmanov
Keyword(s):  
Upper Bounds ◽  
Burnside Problem ◽  
Restricted Burnside Problem

UPPER BOUNDS IN THE RESTRICTED BURNSIDE PROBLEM II

1996 ◽  
Vol 06 (06) ◽  
pp. 735-744 ◽  
Author(s):  
MICHAEL VAUGHAN-LEE ◽  
E.I. ZELMANOV
Keyword(s):  
Finite Groups ◽  
Prime Power ◽  
Upper Bounds ◽  
Reduction Theorem ◽  
Power Exponent ◽  
Burnside Problem ◽  
Restricted Burnside Problem

We show that if G is a finite m generator group of exponent n, with m>1, then [Formula: see text] This result extends bounds previously obtained for finite groups of prime power exponent. The proof is based on a reduction theorem for the restricted Burnside problem due to Hall and Higman.

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.

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