Groups, Geometry, and Dynamics


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Volume 11, Issue 3, 2017, pp. 879–890
DOI: 10.4171/GGD/417

Published online: 2017-08-22

A sharp threshold for collapse of the random triangular group

Sylwia Antoniuk[1], Ehud Friedgut[2] and Tomasz Łuczak[3]

(1) Adam Mickiewicz University, Poznán, Poland
(2) Weizmann Institute of Science, Rehovot, Israel
(3) Adam Mickiewicz University, Poznán, Poland

The random triangular group $\Gamma (n,p)$ is the group given by a random group presentation with $n$ generators in which every relator of length three is present independently with probability $p$. We show that in the evolution of €$\Gamma (n,p)$ the property of collapsing to the trivial group admits a very sharp threshold.

Keywords: Random group, collapse, sharp threshold, torsion-free

Antoniuk Sylwia, Friedgut Ehud, Łuczak Tomasz: A sharp threshold for collapse of the random triangular group. Groups Geom. Dyn. 11 (2017), 879-890. doi: 10.4171/GGD/417