A nilpotent quotient algorithm for certain infinitely presented groups and its applications

We describe a nilpotent quotient algorithm for a certain class of infinite presentations: the so-called finite L-presentations. We then exhibit finite L-presentations for various examples and report on the application of our nilpotent quotient algorithm to them. As a 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 generalizations of the Fabrykowski-Gupta group, and certain generalizations of the Gupta-Sidki group.