Sylwia Antoniuk: A prompt collapse of the random triangular group

The random triangular group Gamma(n,p) is the group given by a random presentation , where S is a set of n generators and R is a random set of relators such that each relator of length three is present in R independently with probability p. We are interested in the behaviour of the random group in the Gamma(n,p) model when p=p(n) and the number of generators n goes to infinity. In particular, we show that the property of collapsing to the trivial group admits a very sharp threshold.

This is a joint work with Ehud Friedgut, Tomasz Luczak and Jacek Swiatkowski.