Equations in acylindrically hyperbolic groups and verbal closedness

DOI10.4171/GGD/661WikidataQ115481601 ScholiaQ115481601MaRDI QIDQ2102162

Publication date: 28 November 2022

Published in: Groups, Geometry, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.08071

zbMATH Keywords

retract relatively hyperbolic group verbally closed subgroup acylindrically hyperbolic group algebraically closed subgroup equationally Noetherian group equations over a group

Mathematics Subject Classification ID

Geometric group theory (20F65) Hyperbolic groups and nonpositively curved groups (20F67) Algebraic geometry over groups; equations over groups (20F70)

Related Items (max. 100)

Finite and nilpotent strongly verbally closed groups

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Induced quasicocycles on groups with hyperbolically embedded subgroups.
New topological methods to solve equations over groups
Test elements in torsion-free hyperbolic groups.
Makanin-Razborov diagrams over free products.
Virtually free finite-normal-subgroup-free groups are strongly verbally closed
Über Worte \(S_1^{a_1}, S_2^{a_2}, \ldots, S_q^{a_q}\) in einer freien Gruppe mit \(p\) freien Erzeugenden
Enumerating limit groups.
Nullhomologous words in free groups which are not nullhomologous in any proper subgroup
Commutator equations in free groups
Géométrie et théorie des groupes. Les groupes hyperboliques de Gromov. (Geometry and group theory. The hyperbolic groups of Gromov)
The verbal topology of a group
On certain elements of free groups
Algebraic geometry over groups. I: Algebraic sets and ideal theory
Recognizing automorphisms of the free groups
On certain \(C\)-test words for free groups
Two theorems about equationally Noetherian groups
Irreducible affine varieties over a free group. I: Irreducibility of quadratic equations and Nullstellensatz
Test elements and the retract theorem in hyperbolic groups
Contracting elements and random walks
Strongly verbally closed groups
Existentially closed CSA-groups.
Bounded cohomology of subgroups of mapping class groups
Algebraic geometry over groups. II: Logical foundations
Diophantine geometry over groups. I: Makanin-Razborov diagrams
The lower algebraic \(K\)-theory of virtually infinite cyclic groups
Universal solvability of group equations
Abstract homomorphisms from some topological groups to acylindrically hyperbolic groups
A periodicity theorem for acylindrically hyperbolic groups
Makanin-Razborov diagrams for hyperbolic groups
Verbally and existentially closed subgroups of free nilpotent groups.
Existentially closed subgroups of free nilpotent groups.
Normal generation and \(\ell^2\)-Betti numbers of groups.
Algebraically and verbally closed subgroups and retracts of finitely generated nilpotent groups
On free decompositions of verbally closed subgroups in free products of finite groups
Bounded cohomology and isometry groups of hyperbolic spaces
Tight geodesics in the curve complex
Über Automorphismen ebener diskontinuierlicher Gruppen
On algebraically closed groups
Acylindrically hyperbolic groups
Equations over groups
Verbally closed subgroups of free groups
Relatively hyperbolic groups: intrinsic geometry, algebraic properties, and algorithmic problems
Algebraically closed torsion-free nilpotent groups of class 2
Verbally closed virtually free subgroups
Test Words for Automorphisms of Free Groups
GROUPS ACTING ACYLINDRICALLY ON HYPERBOLIC SPACES
Free products of groups are strongly verbally closed
Homomorphisms to acylindrically hyperbolic groups I: Equationally noetherian groups and families
From local to global conjugacy of subgroups of relatively hyperbolic groups
Diophantine geometry over groups VII: The elementary theory of a hyperbolic group
Adjunction of Elements To Groups
Algebraically Closed Groups
A Note on Algebraically Closed Groups

This page was built for publication: Equations in acylindrically hyperbolic groups and verbal closedness