scholarly journals Random triangular Burnside groups

2021 ◽  
Author(s):  
Dominik Gruber ◽  
John M. Mackay
Keyword(s):  
Burnside Groups

Infinite Burnside groups of even exponent

1996 ◽  
Vol 60 (3) ◽  
pp. 453-654 ◽  
Author(s):  
I G Lysenok
Keyword(s):  
Burnside Groups

scholarly journals On the geometry of burnside quotients of torsion free hyperbolic groups

2014 ◽  
Vol 24 (03) ◽  
pp. 251-345 ◽  
Author(s):  
Rémi Coulon
Keyword(s):  
Hyperbolic Groups ◽  
Geometrical Approach ◽  
Small Cancellation ◽  
Small Cancellation Theory ◽  
Burnside Groups ◽  
Torsion Free

In this paper, we detail the geometrical approach of small cancellation theory used by Delzant and Gromov to provide a new proof of the infiniteness of free Burnside groups and periodic quotients of torsion-free hyperbolic groups.

THE WHITEHEAD ASPHERICITY CONJECTURE AND PERIODIC GROUPS

1999 ◽  
Vol 09 (05) ◽  
pp. 529-538 ◽  
Author(s):  
S. V. IVANOV
Keyword(s):  
Group Presentation ◽  
Burnside Groups ◽  
Periodic Groups ◽  
Whitehead Conjecture

The Whitehead asphericity conjecture claims that if [Formula: see text] is an aspherical group presentation, then for every [Formula: see text] the subpresentation [Formula: see text] is also aspherical. This conjecture is generalized for presentations of groups with periodic elements by introducing almost aspherical presentations (for example, every one-relator group is almost aspherical). It is proven that the generalized Whitehead asphericity conjecture (which claims that every subpresentation of an almost aspherical presentation is also almost aspherical) is equivalent to the original Whitehead conjecture. It is also proven that the generalized Whitehead asphericity conjecture holds for Ol'shanskii's presentations of free Burnside groups of large odd exponent, presentations of Tarski monsters and others.

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