A Nilpotent Quotient Algorithm for Certain Infinitely Presented Groups and its Applications

We describe a nilpotent quotient algorithm for a certain type of infinite presentations: the so-called finite L-presentations. We then exhibit finite L-presentations for various interesting groups and report on the application of our nilpotent quotient algorithm to them. As result, we obtain conjectural descriptions of the lower central series structure of various interesting groups including the Grigorchuk supergroup, the Brunner-Sidki-Vieira group, the Basilica group, certain generalized FabrykowskiGupta groups and certain generalized Gupta-Sidki groups.