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

TL;DR

This paper introduces an algorithm to approximate the Schur multiplier of certain infinitely presented groups using nilpotent quotients, and applies it to analyze various self-similar groups.

Contribution

It presents a novel algorithm for computing Schur multipliers of infinitely presented groups and applies it to several complex self-similar groups.

Findings

Successfully computed Schur multipliers for multiple self-similar groups

Provided new insights into the structure of these groups' Schur multipliers

Demonstrated the effectiveness of nilpotent quotients in approximating the Schur multiplier

Abstract

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.