scholarly journals A combination theorem for cubulation in small cancellation theory over free products

2017 ◽  
Vol 67 (4) ◽  
pp. 1613-1670 ◽  
Author(s):  
Alexandre Martin ◽  
Markus Steenbock
Keyword(s):  
Small Cancellation ◽  
Free Products ◽  
Small Cancellation Theory

On small cancellation theory over H.N.N. extensions

1983 ◽  
Vol 94 (1-2) ◽  
pp. 25-47 ◽  
Author(s):  
J. Perraud
Keyword(s):  
Word Problem ◽  
Finite Subset ◽  
Decision Problems ◽  
Normal Closure ◽  
Small Cancellation ◽  
Free Products ◽  
Cancellation Condition ◽  
Small Cancellation Theory ◽  
Amalgamated Free Products ◽  
Small Cancellation Condition

SynopsisSmall cancellation theory has been extended to symmetrized subsets of free products, amalgamated free products and Higman-Neumann-Neumann (H.N.N.) extensions. We though that it was possible to obtain results on decision problems if we could define small cancellation conditions for finite subsets.Sacerdote and Schupp (1974) defined the small cancellation condition C'(l/6) for symmetrized subsets of an H.N.N. extension. We define this condition for finite subsets, with the following properties:For each finite subset X, there is a symmetrized subset X1 with the same normal closure and, if X1 satisfies C'(l/6), then X satisfies C'(l/6).For some H.N.N. extensions, we can decide whether any finite subset satisfies C'(l/6), and, in this case, we can solve the word problem for the corresponding quotient.

The word problem for small cancellation quotients of groups acting on trees

1992 ◽  
Vol 121 (3-4) ◽  
pp. 361-374
Author(s):  
R. M. S. Mahmud
Keyword(s):  
Word Problem ◽  
Small Cancellation ◽  
Free Products ◽  
Small Cancellation Theory ◽  
Products Of Groups ◽  
Groups Acting On Trees ◽  
Free Products With Amalgamation

SynopsisThe small cancellation theory over free products with amalgamation and HNN groups is extended to groups acting on trees in which the action with inversions is possible. This will include the case of tree products of groups and treed-HNN groups.

SOME REMARKS ON ONE-RELATOR AMALGAMATED FREE PRODUCTS II

2006 ◽  
Vol 16 (01) ◽  
pp. 1-15 ◽  
Author(s):  
ARYE JUHÁSZ
Keyword(s):  
Free Product ◽  
Normal Closure ◽  
Small Cancellation ◽  
Free Products ◽  
Small Cancellation Theory ◽  
Amalgamated Free Products

We consider quotients of the free product G of groups A and B, amalgamated along a group C, which is malnormal in A and in B. We concentrate on quotients H of G by the normal closure of a single relator which is a power of a word. We show that a part of the results which are true for the corresponding one relator free products hold true for H. We reduce the problems to the free product case and use small cancellation theory.

On a conjecture in Artin groups

2021 ◽  
pp. 1-25
Author(s):  
Arye Juhász
Keyword(s):  
Artin Group ◽  
Two Dimensional ◽  
Artin Groups ◽  
Small Cancellation ◽  
Small Cancellation Theory ◽  
Infinite Type ◽  
Trivial Center

It is conjectured that an irreducible Artin group which is of infinite type has trivial center. The conjecture is known to be true for two-dimensional Artin groups and for a few other types of Artin groups. In this work, we show that the conjecture holds true for Artin groups which satisfy a condition stronger than being of infinite type. We use small cancellation theory of relative presentations.

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.

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