Product set growth in groups and hyperbolic geometry

Abstract

Generalising results of Razborov and Safin, and answering a question of Button, we prove that for every hyperbolic group there exists a constant $\alpha >0$ such that for every finite subset $U$ that is not contained in a virtually cyclic subgroup $|U^n|⩾(\alpha |U|{)}^{[(n+1)/2]}$. Similar estimates are established for groups acting acylindrically on trees or hyperbolic spaces.

arXiv comment38 pages, accepted for publication by the Journal of Topology

References in corpus (7)

• Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces
• Small cancellation theory and Burnside problem
• Freiman's theorem for solvable groups
• Curvature-Free Margulis Lemma for Gromov-Hyperbolic Spaces
• On the joint spectral radius for isometries of non-positively curved spaces and uniform growth
• Partial periodic quotient of groups acting on a hyperbolic space
• Small cancellation theory over Burnside groups

Cited by in corpus (6)

• On the joint spectral radius for isometries of non-positively curved spaces and uniform growth
• Topological volumes of fibrations: A note on open covers
• The rates of growth in a hyperbolic group
• Product set growth in Burnside groups
• Product set growth in virtual subgroups of mapping class groups
• Large deviation principles for non-elementary random walks on hyperbolic spaces