A sharp threshold for collapse of the random triangular group

Abstract

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.

arXiv comment12 pages, revised version