Approximating the Schur multiplier of certain infinitely presented groups via nilpotent quotients

We describe an algorithm for computing successive quotients of the Schur multiplier $M(G)$ for a group $G$ given by an invariant finite $L$-presentation. As application, we investigate the Schur multipliers of various self-similar groups such as the Grigorchuk super-group, the generalized Fabrykowski-Gupta groups, the Basilica group and the Brunner-Sidki-Vieira group.