Random triangular Burnside groups

Abstract

We introduce a model for random groups in varieties of $n$-periodic groups as $n$-periodic quotients of triangular random groups. We show that for an explicit $d_{\mathrm{crit}}\in (1/3,1/2)$, for densities $d\in (1/3,d_{\mathrm{crit}})$ and for $n$ large enough, the model produces \emph{infinite} $n$-periodic groups. As an application, we obtain, for every fixed large enough $n$, for every $p\in (1,\infty )$ an infinite $n$-periodic group with fixed points for all isometric actions on $L^p$-spaces. Our main contribution is to show that certain random triangular groups are uniformly acylindrically hyperbolic.

v1: 9 pages, 1 figure; v2: 14 pages, 1 figure. Expanded exposition, final version

References in corpus (5)

• Random groups, random graphs and eigenvalues of p-Laplacians
• Freiheitssatz and phase transition for the density model of random groups
• Small cancellation theory over Burnside groups
• Group cubization (with an appendix by Mikael Pichot)
• Infinite periodic groups of even exponents