• Corpus ID: 118401670

A Note on Invariantly Finitely $L$-Presented Groups

@article{Hartung2012ANO,
  title={A Note on Invariantly Finitely \$L\$-Presented Groups},
  author={Ren{\'e} Hartung},
  journal={arXiv: Group Theory},
  year={2012}
}
In the first part of this note, we introduce Tietze transformations for $L$-presentations. These transformations enable us to generalize Tietze's theorem for finitely presented groups to invariantly finitely $L$-presented groups. Moreover, they allow us to prove that `being invariantly finitely $L$-presented' is an abstract property of a group which does not depend on the generating set. In the second part of this note, we consider finitely generated normal subgroups of finitely presented… 
1 Citations
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References

SHOWING 1-10 OF 21 REFERENCES
A Reidemeister-Schreier theorem for finitely $L$-presented groups
We prove a variant of the well-known Reidemeister-Schreier theorem for finitely $L$-presented groups. More precisely, we prove that each finite index subgroup of a finitely $L$-presented group is
Subgroups of finitely presented groups
  • G. Higman
  • Mathematics
    Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1961
The main theorem of this paper states that a finitely generated group can be embedded in a finitely presented group if and only if it has a recursively enumerable set of defining relations. It
Coset Enumeration for certain Infinitely Presented Groups
TLDR
This algorithm shows that the subgroup membership problem for finite index subgroups in a finitely $L$-presented group is decidable.
Investigating self-similar groups using their finite $L$-presentation
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
INDICABLE GROUPS AND ENDOMORPHIC PRESENTATIONS
  • M. Benli
  • Mathematics
    Glasgow Mathematical Journal
  • 2011
Abstract In this paper we look at presentations of subgroups of finitely presented groups with infinite cyclic quotients. We prove that if H is a finitely generated normal subgroup of a finitely
On a 2-generated infinite 3-group: The presentation problem
A Nilpotent Quotient Algorithm for Certain Infinitely Presented Groups and its Applications
TLDR
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.
Topics in Geometric Group Theory
In this book, Pierre de la Harpe provides a concise and engaging introduction to geometric group theory, a new method for studying infinite groups via their intrinsic geometry that has played a major
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 ) of a group G given by an invariant finite L -presentation. As applications, we investigate the Schur
Combinatorial Group Theory
Chapter I. Free Groups and Their Subgroups 1. Introduction 2. Nielsen's Method 3. Subgroups of Free Groups 4. Automorphisms of Free Groups 5. Stabilizers in Aut(F) 6. Equations over Groups 7.
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