Small cancellation theory over Burnside groups

@article{Coulon2017SmallCT,
  title={Small cancellation theory over Burnside groups},
  author={R{\'e}mi Coulon and Dominik Gruber},
  journal={Advances in Mathematics},
  year={2017}
}
View PDF on arXiv
8 Citations
Background Citations
3

Figures from this paper

8 Citations

Random triangular Burnside groups

We introduce a model for random groups in varieties of n-periodic groups as n-periodic quotients of triangular random groups. We show that for an explicit dcrit ∈ (1/3, 1/2), for densities d ∈ (1/3,…

Product set growth in groups and hyperbolic geometry

Generalising results of Razborov and Safin, and answering a question of Button, we prove that for every hyperbolic group there exists a constant α>0 such that for every finite subset U that is not…

Actions of small cancellation groups on hyperbolic spaces

We generalize Gruber–Sisto’s construction of the coned-off graph of a small cancellation group to build a partially ordered set $${\mathcal {TC}}$$ TC of cobounded actions of a given small…

Infinite periodic groups of even exponents

We give a new proof that free Burnside groups of sufficiently large even exponents are infinite. The method can also be used to study (partially) periodic quotients of any group which admits an…

The geometry of generalized loxodromic elements

We explore geometric conditions which ensure a given element of a finitely generated group is, or fails to be, generalized loxodromic; as part of this we prove a generalization of Sisto's result that…

Morse quasiflats I

This paper introduces a number of alternative definitions of Morse quasiflats, and under appropriate assumptions on the ambient space it is shown that they are equivalent and quasi-isometry invariant; it also gives a variety of examples.

The extrinsic primitive torsion problem

Let $P_k$ be the subgroup generated by $k$th powers of primitive elements in $F_r$, the free group of rank $r$. We show that $F_2/P_k$ is finite if and only if $k$ is $1$, $2$, or $3$. We also fully…

Actions of small cancellation groups on hyperbolic spaces

We generalize Gruber–Sisto’s construction of the coned-off graph of a small cancellation group to build a partially ordered set TC\documentclass[12pt]{minimal} \usepackage{amsmath}…

References

SHOWING 1-10 OF 53 REFERENCES

Periodic products of groups

In this paper we provide an overview of the results relating to the n-periodic products of groups that have been obtained in recent years by the authors of the present paper, as well as some results…

Small cancellation labellings of some infinite graphs and applications

We construct small cancellation labellings for some infinite sequences of finite graphs of bounded degree. We use them to define infinite graphical small cancellation presentations of groups. This…

Negative curvature in graphical small cancellation groups

We use the interplay between combinatorial and coarse geometric versions of negative curvature to investigate the geometry of infinitely presented graphical $Gr'(1/6)$ small cancellation groups. In…

Contracting geodesics in infinitely presented graphical small cancellation groups

We study contraction properties of geodesics in infinitely presented graphical $Gr'(1/6)$ small cancellation groups. We show that every degree of contraction can be achieved by a geodesic in a…

Rips–Segev torsion-free groups without the unique product property

The Free Burnside Groups of Sufficiently Large exponents

  • S. Ivanov
  • Mathematics
    Int. J. Algebra Comput.
  • 1994
The paper contains a self-contained construction of m-generated free Burnside groups B(m, n) of exponent n, where m>1, n≥248 and n is either odd or divisible by 29. As a corollary, one gets that the…

Unsolvable Problems About Small Cancellation and Word Hyperbolic Groups

We apply a construction of Rips to show that a number of algorithmic problems concerning certain small cancellation groups and, in particular, word hyperbolic groups, are recursively unsolvable.…

Cubulating small cancellation groups

AbstractWe study the B(6) and B(4)-T(4) small cancellation groups. These classes include the usual C’(1/6) and C’(1/4)-T(4) metric small cancellation groups. We show that every finitely presented…

CEP-Subgroups of Free Burnside Groups of Large Odd Exponents

Abstract For sufficiently large odd exponent n we construct a CEP-subgroup isomorphic to a free Burnside group B(∞, n) with infinite number of generators in the free Burnside group B(2, n) on two…

Groups with graphical C(6) and C(7) small cancellation presentations

We extend fundamental results of small cancellation theory to groups whose presentations satisfy the generalizations of the classical C(6) and C(7) conditions in graphical small cancellation theory.…
...