Coset enumeration for certain infinitely presented groups

摘要

We describe an algorithm that computes the index of a finitely generated subgroup in a finitely L-presented group provided that this index is finite. This algorithm shows that the subgroup membership problem for finite index subgroups in a finitely L-presented group is decidable. As an application, we consider the low-index subgroups of some self-similar groups including the Grigorchuk group, the twisted twin of the Grigorchuk group, the Grigorchuk super-group, and the Hanoi 3-group.