Coset Enumeration for certain Infinitely Presented Groups

  title={Coset Enumeration for certain Infinitely Presented Groups},
  author={Ren{\'e} Hartung},
  journal={Int. J. Algebra Comput.},
  • René Hartung
  • Published 1 June 2011
  • Mathematics
  • Int. J. Algebra Comput.
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 
A Reidemeister-Schreier theorem for finitely $L$-presented groups
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Self-similar groups provide a rich source of groups with interesting properties; e.g., infinite torsion groups (Burnside groups) and groups with an intermediate word growth. Various self-similar
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This dissertation is devoted to the study of self-similar groups and related topics. It consists of three parts. The first part is devoted to the study of examples of finitely generated amenable
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Let G be a group and h, g ∈ G. The 2-tuple (h, g) is said to be an n-Engel pair, n ≥ 2, if h = [h,n g], g = [g,n h] and h ≠ 1. In this paper, we prove that if (h, g) is an n-Engel pair, hgh-2gh = ghg


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  • G. Baumslag
  • Mathematics
    Bulletin of the Australian Mathematical Society
  • 1971
We exhibit a 3-generator metabelian group which is not finitely related but has a trivial multiplicator. 1. The purpose of this note is to establish the exitense of a finitely generated group which
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The use of computers to investigate groups has mainly been restricted to finite groups. In this work, a method is given for finding all subgroups of finite index in a given group, which works equally
A Nilpotent Quotient Algorithm for Certain Infinitely Presented Groups and its Applications
A nilpotent quotient algorithm is described for a certain class of infinite presentations: the so-called finite L-presentations and conjectural descriptions of the lower central series structure of various interesting groups including the Grigorchuk supergroup, the Brunner–Sidki–Vieira group, the Basilica group, and certain generalizations of the Fabrykowski–Gupta group are obtained.
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  • C. Sims
  • Mathematics
    Encyclopedia of mathematics and its applications
  • 1994
1. Basic concepts 2. Rewriting systems 3. Automata and rational languages 4. Subgroups of free products of cyclic groups 5. Coset enumeration 6. The Reidemeister-Schreier procedure 7. Generalized
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Coset enumeration, based on the methods described by Todd and Coxeter, is one of the basic tools for investigating finitely presented groups. The process is not well understood, and various
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