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COSET ENUMERATION FOR CERTAIN INFINITELY PRESENTED GROUPS

RENÉ HARTUNG

Mathematisches Institut, Georg-August Universität zu Göttingen, Bunsenstrasse 3–5, 37073 Göttingen, Germany

https://doi.org/10.1142/S0218196711006637Cited by:5 (Source: Crossref)

Abstract

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.

Keywords:

AMSC: 20F05, 20F10, 20E07, 20E28, 20-04

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