77 citations · 224 across the 14 of their papers we have counts for
11 papers · 1 filter
On what finitely generated (left-orderable) simple groups can know about their subgroups
Arman Darbinyan, Markus Steenbock
In this paper, we survey some of the recent advances on embeddings into finitely generated (left-orderable) simple group such that the overgroup preserves algorithmic, geometric, o…
Random Quotients of Free Products
Eduard Einstein, Suraj Krishna M S, MurphyKate Montee +2
We introduce a density model for random quotients of a free product of finitely generated groups. We prove that a random quotient in this model has the following properties with ov…
Uniform growth in small cancellation groups
Xabier Legaspi, Markus Steenbock
An open question asks whether every group acting acylindrically on a hyperbolic space has uniform exponential growth. We prove that the class of groups of uniform uniform exponenti…
Subgroups and diversity of left-orderable small cancellation groups
Markus Steenbock
We arrange classical small cancellation constructions to produce left-orderable groups: we show that every finitely generated group is the quotient of a left-ordered small cancella…
Product set growth in Burnside groups
Rémi Coulon, Markus Steenbock
Given a periodic quotient of a torsion-free hyperbolic group, we provide a fine lower estimate of the growth function of any sub-semi-group. This generalizes results of Razborov an…
Embeddings into left-orderable simple groups
Arman Darbinyan, Markus Steenbock
We prove that every countable left-ordered group embeds into a finitely generated left-ordered simple group. Moreover, if the first group has a computable left-order, then the simp…
Product set growth in groups and hyperbolic geometry
Thomas Delzant, Markus Steenbock
Generalising results of Razborov and Safin, and answering a question of Button, we prove that for every hyperbolic group there exists a constant such that for every finite su…
A combination theorem for cubulation in small cancellation theory over free products
Alexandre Martin, Markus Steenbock
We prove that a group obtained as a quotient of the free product of finitely many cubulable groups by a finite set of relators satisfying the classical --small cancellatio…
Finite index subgroups without unique product in graphical small cancellation groups
Dominik Gruber, Alexandre Martin, Markus Steenbock
We construct torsion-free hyperbolic groups without unique product whose subgroups up to some given finite index are themselves non-unique product groups. This is achieved by gener…
Rips construction without unique product
Goulnara Arzhantseva, Markus Steenbock
Given a finitely presented group we produce a short exact sequence such that is a torsion-free Gromov hyperbolic grou…
Rips-Segev torsion-free groups without the unique product property
Markus Steenbock
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…