Non-amenable finitely presented torsion-by-cyclic groups

Abstract. – We construct a finitely presented non-amenable group without free non-cyclic subgroups thus providing a finitely presented counterexample to von Neumann’s problem. Our group is an extension of a group of finite exponent n ≫ 1 by a cyclic group, so it satisfies the identity [x,y]n = 1.

• Publication year

  2001

• Venue

  Publications Mathématiques de l'Institut des Hautes Études Scientifiques

• Publication date

  2001-07-03

• Fields of study

  Mathematics

• Identifiers
  DOI 10.1090/S1079-6762-01-00095-6arXiv math/0208237
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Influence of cultivation temperature on the ligninolytic activity of selected fungal strains

  2006influential reference
• On HNN-extensions in the class of groups of large odd exponent

  2002cited by this paper
• Open Problems in Infinite Dimensional Topology

  2001cited by this paper
• Embeddings of relatively free groups into finitely presented groups

  2000cited by this paper
• Isoperimetric and isodiametric functions of groups

  1998cited by this paper
• Isoperimetric functions of groups and computational complexity of the word problem

  1998cited by this paper
• Пример конечно определенной аменабельной группы, не принадлежащей классу $EG$@@@An example of a finitely presented amenable group not belonging to the class $EG$

  1998cited by this paper
• Length and Area Functions on Groups and Quasi-Isometric Higman Embeddings

  1998influential reference
• An example of a finitely presented amenable group not belonging to the class EG

  1998cited by this paper
• Hyperbolic groups and their quotients of bounded exponents

  1996cited by this paper
• Algorithmic Problems in Varieties

  1995cited by this paper
• The SQ-universality of hyperbolic groups

  1995cited by this paper
• Geometry of Defining Relations in Groups

  1991cited by this paper
• PROBLEMS OF BURNSIDE TYPE AND THE FINITE BASIS PROPERTY IN VARIETIES OF SEMIGROUPS

  1988cited by this paper
• Groups of piecewise linear homeomorphisms of the real line

  1985cited by this paper
• RANDOM WALKS ON FREE PERIODIC GROUPS

  1983influential reference
• Cogrowth and amenability of discrete groups

  1982cited by this paper
• AN INFINITE GROUP WITH SUBGROUPS OF PRIME ORDERS

  1981cited by this paper
• The Burnside problem and identities in groups

  1979cited by this paper
• Algebraic theory of semigroups

  1979cited by this paper
• Combinatorial Group Theory

  1977cited by this paper
• Unsolved Problems in Group Theory

  1976cited by this paper
• Invariant means on topological groups and their applications

  1969cited by this paper
• INFINITE PERIODIC GROUPS. I

  1968cited by this paper
• The Algebraic Theory of Semigroups, Vol. I

  1964cited by this paper
• Zur Theorie der meßbaren Gruppen

  1960cited by this paper
• Symmetric random walks on groups

  1959cited by this paper
• Full Banach Mean Values on Countable groups.

  1959cited by this paper
• On groups with full Banach mean value

  1955cited by this paper
• Grundzüge der Mengenlehre

  1915cited by this paper
• Zur allgemeinen Theorie des Masses

  year unknowninfluential reference
• Sur la décomposition des ensembles de points en parties respectivement congruentes

  year unknowninfluential reference

• Entanglement in typical states of Chern-Simons theory

  2025cites this paper
• Nearby special Lagrangians

  2025cites this paper
• Remembering Mark Sapir

  2024cites this paper
• Amenability problem for Thompson's group $F$: state of the art

  2023cites this paper
• Полугруппа путей на семействе равномерно эллиптических комплексов

  2023cites this paper
• A Semigroup of Paths on a Sequence of Uniformly Elliptic Complexes

  2023cites this paper
• BOOK REVIEWS

  2023cites this paper
• Finiteness properties of some groups of piecewise projective homeomorphisms

  2022cites this paper
• An n-adic generalization of the Lodha–Moore group

  2022cites this paper
• Cayley graphs of R. Thompson's group F: new estimates for the density

  2022cites this paper
• R. Thompson’s group and the amenability problem

  2022cites this paper
• A GENERALIZATION OF THE LODHA–MOORE GROUP

  2022cites this paper
• Evacuation schemes on Cayley graphs and non-amenability of groups

  2021cites this paper
• Generic algebraic properties in spaces of enumerated groups

  2020cites this paper
• Groups finitely presented in Burnside varieties

  2020cites this paper
• Torsion Subgroups of Groups with Quadratic Dehn Function

  2020cites this paper
• A generic negative solution to the von Neumann-Day problem

  2020cites this paper
• Deterministic coloring of the sequence of complexes

  2020cites this paper
• A nonamenable type F∞ group of piecewise projective homeomorphisms

  2020cites this paper
• Torsion Subgroups of Groups with Cubic Dehn Function

  2020influential citation
• The complexes with property of uniform ellipticity

  2019cites this paper
• Subgroups of groups finitely presented in Burnside varieties

  2019influential citation
• Extensive amenability and a Tits alternative for topological full groups

  2019cites this paper
• Bounded Depth Ascending HNN Extensions and $\unicode[STIX]{x1D70B}_{1}$-Semistability at infinity

  2019cites this paper
• Finitely presented nilsemigroups: complexes with the property of uniform ellipticity

  2019cites this paper
• BOUNDED DEPTH ASCENDING HNN EXTENSIONS AND π1-SEMISTABILITY

  2019cites this paper
• On the density of Cayley graphs of R.Thompson's group F in symmetric generators

  2019cites this paper
• A Geometric Approach to the Modified Milnor Problem

  2018cites this paper
• A notion of effectiveness for subshifts on finitely generated groups.

  2018cites this paper
• On amenability of two-generator groups

  2018cites this paper
• The Burnside problem for locally compact groups

  2018cites this paper
• Non-triviality of the Poisson boundary of random walks on the group HpZq of Monod

  2018influential citation
• Non-triviality of the Poisson boundary of random walks on the group $H(\mathbb{Z})$ of Monod

  2018cites this paper
• GROUP ACTIONS ON 1-MANIFOLDS: A LIST OF VERY CONCRETE OPEN QUESTIONS

  2017cites this paper
• On geodesic flows with symmetries and closed magnetic geodesics on orbifolds

  2017cites this paper
• Schreier Graphs of Thompson's Group T

  2017cites this paper
• Bounded Depth Ascending HNN Extensions and $\pi_1$-Semistability at $\infty$

  2017cites this paper
• Groups Acting on Dendrons

  2016cites this paper
• Groups Acting on Dendrons

  2016cites this paper
• Introduction to Thompson’s group F

  2016cites this paper
• A nonamenable finitely presented group of piecewise projective homeomorphisms

  2016cites this paper
• Bounded cohomology of discrete groups

  2016cites this paper
• New residually amenable groups, permanence properties, and metric approximations

  2016cites this paper
• Periodic points for amenable group actions on dendrites

  2016cites this paper
• A New Class of Generalized Thompson's Groups and Their Normal Subgroups

  2016cites this paper
• Finiteness Properties And Piecewise Projective Homeomorphisms

  2015influential citation
• Construction of Infinite Finitely Presented Nilsemigroup

  2014cites this paper
• Richard Thompson group F is not amenable

  2014cites this paper
• $C^\ast$-simple groups without free subgroups

  2014cites this paper
• Ergodic Theory and Dynamical Systems

  2014cites this paper
• Justin Tatch Moore Hindman ’ s Theorem , Ellis ’ s Lemma , and Thompson ’ s group

  2014cites this paper
• A nonamenable type $F_{\infty}$ group of piecewise projective homeomorphisms

  2014cites this paper
• A notion of effectiveness for subshifts on finitely generated groups

  2014cites this paper
• Combinatorial algebra : syntax and semantics

  2014cites this paper
• Inner amenability for groups and central sequences in factors

  2013cites this paper
• A finitely presented group of piecewise projective homeomorphisms

  2013cites this paper
• Acylindrical hyperbolicity of groups acting on trees

  2013cites this paper
• Groups of piecewise projective homeomorphisms

  2012cites this paper
• Universal Borel actions of countable groups

  2012cites this paper
• Some arithmetic groups that do not act on the circle

  2012cites this paper
• Nonassociative Ramsey Theory and the amenability of Thompson's group

  2012cites this paper
• Notes on the Sigma invariants

  2012cites this paper
• Amenable groups without finitely presented amenable covers

  2012cites this paper
• SPACE FUNCTIONS OF GROUPS

  2012cites this paper
• SPACE FUNCTIONS OF GROUPS

  2012cites this paper
• Homology of Group Von Neumann Algebras

  2012cites this paper
• The Burnside problem and related topics

  2011cites this paper
• The girth alternative for mapping class groups

  2011cites this paper
• On the cogrowth of Thompson's group F

  2011cites this paper
• Coset Enumeration for certain Infinitely Presented Groups

  2011cites this paper
• Amenability and Ramsey Theory

  2011cites this paper
• Invariant percolation and measured theory of nonamenable groups

  2011cites this paper
• On the Dixmier problem (Seminar report after Monod-Ozawa, JFA 2010)

  2011cites this paper
• Milnor's Problem on the Growth of Groups and its Consequences

  2011cites this paper
• Schreier graphs of actions of Thompson’s group $$F$$F on the unit interval and on the Cantor set

  2011cites this paper
• Aspherical groups and manifolds with extreme properties

  2011cites this paper
• On normal subgroups in the periodic products of S.I. Adian

  2011influential citation
• On CEP-subgroups of n-periodic products

  2011cites this paper
• The groups of self‐homotopy equivalences and the Tits alternative

  2011cites this paper
• INVARIANT PERCOLATION AND MEASURED THEORY OF NONAMENABLE GROUPS [ after

  2011cites this paper
• Lecture notes on ergodic theory

  2011cites this paper
• The Burnside problem and related topics

  2010cites this paper
• Проблема Бернсайда и связанные с ней вопросы@@@The Burnside problem and related topics

  2010cites this paper
• Amenability properties of Fourier algebras and Fourier-Stieltjes algebras: a survey

  2010cites this paper
• Cellular Automata and Groups

  2010cites this paper
• Groups of positive weighted deficiency and their applications

  2010cites this paper
• Behavior of geodesic rays in spaces with geometric group actions

  2010cites this paper
• Approximating the first $L^2$-betti number of residually finite groups

  2010cites this paper
• Asymptotic invariants, complexity of groups and related problems

  2010influential citation
• Space functions of groups

  2010cites this paper
• Monomorphisms of free Burnside groups

  2009cites this paper
• О мономорфизмах свободных бернсайдовых групп@@@Monomorphisms of Free Burnside Groups

  2009cites this paper
• Amenable actions of discrete groups

  2009cites this paper
• On the Question of the Thompson Group

  2009cites this paper
• A new metric criterion for non-amenability I

  2009cites this paper
• On the Universal Theory of Torsion and Lacunary Hyperbolic Groups

  2009cites this paper
• On Dehn Functions of Infinite Presentations of Groups

  2009cites this paper
• Amenability of linear-activity automaton groups

  2009cites this paper
• Rank gradient and torsion groups

  2009cites this paper
• Closed geodesics in compact Riemannian good orbifolds and horizontal periodic geodesics of Riemannian foliations

  2009cites this paper