Year: 2024
Type: preprint
Abstract: Random groups of density d<\frac{1}{2} are infinite hyperbolic, and of density d>\frac{1}{2} are finite. We prove that for any given system of equations Σ, all the solutions of Σover a random group of density d<\frac{1}{2} are projected from solutions of Σover the free group F_{k}, with overwhelming probability, where k is the rank of the group. We conclude that any given sentence in the Boolean algebra of universal sentences, is a truth sentence over F_{k} if and only if it is a truth sentence over random groups of density d<\frac{1}{2}, with overwhelming probability.
Source: arXiv (Cornell University)
Author: Massalha, Sobhi
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4400024968