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arXiv · 1804.01867

Product set growth in groups and hyperbolic geometry

Thomas Delzant·Markus Steenbock
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Abstract

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

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Thomas Delzant, Markus Steenbock. 2020-04-27. Product set growth in groups and hyperbolic geometry. https://doi.org/10.1112/topo.12156

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