Related papers: On a small cancellation theorem of Gromov

We explain and generalise a construction due to Gromov to realise geometric small cancellation groups over graphs of groups as fundamental groups of non-positively curved 2-dimensional complexes of groups. We then give conditions so that…

We prove a combination theorem for hyperbolic groups, in the case of groups acting on complexes displaying combinatorial features reminiscent of non-positive curvature. Such complexes include for instance weakly systolic complexes and…

Gromov (2003) constructed finitely generated groups whose Cayley graphs contain all graphs from a given infinite sequence of expander graphs of unbounded girth and bounded diameter-to-girth ratio. These so-called Gromov monster groups…

We generalize the graphical small cancellation theory of Gromov to a graphical small cancellation theory over the free product. We extend Gromov's small cancellation theorem to the free product. We explain and generalize Rips-Segev's…

This note is intended as an introduction to two previous works respectively by Dahmani, Guirardel, Osin, and by Cantat, Lamy. We give two proofs of a Small Cancellation Theorem for groups acting on a simplicial tree. We discuss the…

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 technique allows us to provide examples of…

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

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. Using these graphical small cancellation…

In a pair of recent papers (one to appear and one forthcoming), the author develops a general version of small cancellation theory applicable in higher dimensions, and then applies this theory to the Burnside groups of sufficiently large…

In the present paper we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free group and introduce three axioms for the corresponding…

We generalize the small cancellation theory over hyperbolic groups developed by Olshanskii to the case of relatively hyperbolic groups. This allows us to construct infinite finitely generated groups with exactly $n$ conjugacy classes for…

We construct an uncountable family of groups of type $FP$. In contrast to every previous construction of non-finitely presented groups of type $FP$ we do not use Morse theory on cubical complexes; instead we use Gromov's graphical small…

We prove the Haagerup property (= Gromov's a-T-menability) for finitely generated groups defined by infinite presentations satisfying the graphical C'(lambda)-small cancellation condition with respect to graphs endowed with a compatible…

The theory of small cancellation groups is well known. In this paper we introduce the notion of Group-like Small Cancellation Ring. This is the main result of the paper. We define this ring axiomatically, by generators and defining…

We study actions of (infinitely presented) graphical small cancellation groups on the Gromov boundaries of their coned-off Cayley graphs. We show that a class of graphical small cancellation groups, including (infinitely presented)…

We show that finite Milnor-Witt correspondences satisfy a cancellation theorem with respect to the pointed multiplicative group scheme. This has several notable applications in the theory of Milnor-Witt motives and Milnor-Witt motivic…

This note contains a new combinatorial proof of Cramer's rule based on the Gessel-Viennot-Lindstrom Lemma.

This paper gives a self-contained group-theoretic proof of a dual version of a theorem of Ore on distributive intervals of finite groups. We deduce a bridge between combinatorics and representations in finite group theory.

We establish a relative version of Gromov's Vanishing Theorem in the presence of amenable open covers with small multiplicity, extending a result of Li, L\"oh, and Moraschini. Our approach relies on Gromov's theory of multicomplexes.

We give a new proof of the main theorem in the theory of C(6) small cancellation complexes. We prove the fundamental theorem of cubical small cancellation theory for C(9) cubical small cancellation complexes.