A prompt collapse of the random triangular group

Graphs, Hypergraphs, and Computing

25 March 14:00 - 15:00

Sylwia Antoniuk - Adam Mickiewicz University

The random triangular group Gamma(n,p) is the group given by a random presentation <S | R> , 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.
Magnus M. Halldorsson
Reykjavik University
Klas Markström
Umeå University
Andrzej Rucinski
Adam Mickiewicz University
Carsten Thomassen
Technical University of Denmark, DTU


Klas Markström


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