Uniform growth in hyperbolic groups

DOI10.5802/aif.1661zbMath0914.20033OpenAlexW2024793057MaRDI QIDQ1272262

Publication date: 29 November 1998

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1998__48_5_1441_0

zbMATH Keywords

entropy growth rates negatively curved groups word hyperbolic groups finitely generated groups finitely presented groups word metrics symmetric generating sets hyperbolic elements

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Topological methods in group theory (57M07)

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Compactness and Finiteness Results for Gromov-Hyperbolic Spaces ⋮ Exponential growth rates of free and amalgamated products. ⋮ Amenability and non-uniform growth of some directed automorphism groups of a rooted tree ⋮ Lower bound on growth of non-elementary subgroups in relatively hyperbolic groups ⋮ Growth of periodic quotients of hyperbolic groups ⋮ Examples of uniform exponential growth in algebras ⋮ The rates of growth in a hyperbolic group ⋮ Hierarchically hyperbolic groups and uniform exponential growth ⋮ Property RD and the classification of traces on reduced group C∗-algebras of hyperbolic groups ⋮ Discrete groups of packed, non-positively curved, Gromov hyperbolic metric spaces ⋮ Uniform growth of groups acting on Cartan-Hadamard spaces. ⋮ Groups acting on CAT(0) cube complexes with uniform exponential growth ⋮ Acylindrically hyperbolic groups with exotic properties ⋮ Unnamed Item ⋮ Makanin-Razborov diagrams for hyperbolic groups ⋮ Algebraic ranks of CAT(0) groups. ⋮ Some finiteness results for groups with bounded algebraic entropy. ⋮ Divergence in lattices in semisimple Lie groups and graphs of groups ⋮ Groups acting on tree-graded spaces and splittings of relatively hyperbolic groups. ⋮ Recognizing a relatively hyperbolic group by its Dehn fillings ⋮ On the geometry of burnside quotients of torsion free hyperbolic groups ⋮ Some finiteness results for groups with bounded algebraic entropy. ⋮ Algebraic entropy of elementary amenable groups. ⋮ Hypercontractivity in finite-dimensional matrix algebras ⋮ On uniform exponential growth for linear groups. ⋮ Rank-one isometries of buildings and quasi-morphisms of Kac-Moody groups. ⋮ On the joint spectral radius for isometries of non-positively curved spaces and uniform growth ⋮ Large groups of deficiency 1. ⋮ Counting subgraphs in fftp graphs with symmetry ⋮ NONVANISHING OF ALGEBRAIC ENTROPY FOR GEOMETRICALLY FINITE GROUPS OF ISOMETRIES OF HADAMARD MANIFOLDS ⋮ Lacunary hyperbolic groups. With an appendix by Michael Kapovich and Bruce Kleiner. ⋮ Uniform nonamenability of subgroups of free Burnside groups of odd period. ⋮ NONVANISHING OF ALGEBRAIC ENTROPY FOR GEOMETRICALLY FINITE GROUPS OF ISOMETRIES OF HADAMARD MANIFOLDS ⋮ Elements of uniformly bounded word-length in groups ⋮ Subgroups generated by two pseudo-Anosov elements in a mapping class group. II. Uniform bound on exponents ⋮ Growth of relatively hyperbolic groups ⋮ Abstract homomorphisms from some topological groups to acylindrically hyperbolic groups ⋮ Random walks on hyperbolic spaces: concentration inequalities and probabilistic Tits alternative ⋮ Uniform non-amenability ⋮ Growth of discrete groups of isometries in negative curvature: a gap-property. ⋮ An alternative on the entropy of groups. ⋮ Product set growth in Burnside groups

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