## 8 Citations

### Random triangular Burnside groups

- MathematicsIsrael Journal of Mathematics
- 2021

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

- MathematicsJournal of Topology
- 2020

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

- MathematicsGeometriae Dedicata
- 2020

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

- Mathematics
- 2018

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

- Mathematics
- 2018

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

- Mathematics, Computer ScienceJournal für die reine und angewandte Mathematik (Crelles Journal)
- 2022

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

- MathematicsAlgebraic & Geometric Topology
- 2020

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

- Materials ScienceGeometriae Dedicata
- 2020

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

- Mathematics
- 2017

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

- Mathematics
- 2014

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

- MathematicsGroups, Geometry, and Dynamics
- 2019

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

- Mathematics
- 2016

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…

### The Free Burnside Groups of Sufficiently Large exponents

- MathematicsInt. 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

- Mathematics
- 1994

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

- Mathematics
- 2004

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

- Mathematics
- 2003

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

- Mathematics
- 2012

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.…