English

Ascending Chains of Free Quasiconvex Subgroups

Group Theory 2024-05-24 v1 Geometric Topology
Authors: Jack Kohav , Nir Lazarovich
View on arXiv ↗ PDF ↗

Abstract

We prove that a hyperbolic group cannot contain a strictly ascending chain of free quasiconvex subgroups of constant rank.

Keywords

hyperbolic groups

Cite

@article{arxiv.2405.13534,
  title  = {Ascending Chains of Free Quasiconvex Subgroups},
  author = {Jack Kohav and Nir Lazarovich},
  journal= {arXiv preprint arXiv:2405.13534},
  year   = {2024}
}

Comments

21 pages

Related papers

View all related →
Group Theory · Mathematics
Ascending Chains in 3-Manifold and Relatively Hyperbolic Groups
Edgar A. Bering, Jakob Heikamp, Jack Kohav, Nir Lazarovich +1
2026-03-31
Group Theory · Mathematics
Ascending chains of free groups in 3-manifold groups
Edgar A. Bering, Nir Lazarovich
2022-02-18
Group Theory · Mathematics
Strictly ascending HNN extensions of finite rank free groups that are linear over Z
J. O. Button
2013-02-22
Geometric Topology · Mathematics
Height in Splitting of Relatively Hyperbolic Groups
Abhijit Pal
2020-11-10
Group Theory · Mathematics
Hyperbolically embedded virtually free subgroups of relatively hyperbolic groups
Yoshifumi Matsuda, Shin-ichi Oguni, Saeko Yamagata
2012-05-23
Group Theory · Mathematics
On the existence of weakly malnormal quasiconvex subgroups of hyperbolic groups
Rakesh Halder, Pranab Sardar
2025-06-26
Group Theory · Mathematics
A non-quasiconvex embedding of relatively hyperbolic groups
Hadi Bigdely
2012-11-13
Geometric Topology · Mathematics
Random extensions of free groups and surface groups are hyperbolic
Samuel J. Taylor, Giulio Tiozzo
2015-01-14
Geometric Topology · Mathematics
Random walks and quasi-convexity in acylindrically hyperbolic groups
C. Abbott, M. Hull
2021-10-04
Group Theory · Mathematics
Freely indecomposable groups acting on hyperbolic spaces
Ilya Kapovich, Richard Weidmann
2007-05-23
Geometric Topology · Mathematics
Quasiconvex Subgroups and Nets in Hyperbolic Groups
Thomas Mack
2007-05-23
Group Theory · Mathematics
Malnormality and join-free subgroups in right-angled Coxeter groups
Hung Cong Tran
2018-10-18
Group Theory · Mathematics
Maximal hyperbolic towers and weight in the theory of free groups
Benjamin Brück
2021-07-01
Group Theory · Mathematics
A non-quasiconvexity embedding theorem for hyperbolic groups
Ilya Kapovich
2009-09-25
Group Theory · Mathematics
Relatively hyperbolic groups with strongly shortcut parabolics are strongly shortcut
Nima Hoda, Suraj Krishna M S
2023-10-24
Group Theory · Mathematics
An example of a non-quasiconvex subgroup of a word hyperbolic group with exotic limit set
Ilya Kapovich
2009-09-25
Group Theory · Mathematics
Embedding Partial HNN Extensions In Ascending HNN Extensions
Hip Kuen Chong, Daniel T. Wise
2024-08-02
Dynamical Systems · Mathematics
Relative growth in hyperbolic groups
Stephen Cantrell, Richard Sharp
2019-12-09
Group Theory · Mathematics
Quasiconvexity in the Relatively Hyperbolic Groups
Victor Gerasimov, Leonid Potyagailo
2011-10-12
Group Theory · Mathematics
Packing subgroups in relatively hyperbolic groups
G. Christopher Hruska, Daniel T. Wise
2014-11-11
Geometric Topology · Mathematics
Propagating quasiconvexity from fibers
Mahan Mj, Pranab Sardar
2021-03-05
Group Theory · Mathematics
Fixed subgroups of automorphisms of relatively hyperbolic groups
Ashot Minasyan, Denis Osin
2012-11-06
Group Theory · Mathematics
On the quasiconvexity of the fixed subgroup of endomorphisms of relatively hyperbolic groups
V. Metaftsis, M. Sykiotis
2016-02-05
Geometric Topology · Mathematics
Random subgroups of acylindrically hyperbolic groups and hyperbolic embeddings
Joseph Maher, Alessandro Sisto
2017-01-03
Group Theory · Mathematics
On Residual Properties of Word Hyperbolic Groups
Ashot Minasyan
2007-05-23