# Algorithms for finitely L-presented groups and their applications to some self-similar groups

@article{Hartung2013AlgorithmsFF, title={Algorithms for finitely L-presented groups and their applications to some self-similar groups}, author={Ren{\'e} Hartung}, journal={Expositiones Mathematicae}, year={2013}, volume={31}, pages={368-384} }

## 2 Citations

## References

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This algorithm shows that the subgroup membership problem for finite index subgroups in a finitely $L$-presented group is decidable.

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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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Computer based techniques for recognizing finitely presented groups are quite powerful. Tools available for this purpose are outlined. They are available both in stand-alone programs and in more…

Hausdorff dimension in a family of self-similar groups

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For every prime p and every monic polynomial f, invertible over p, we define a group Gp, f of p-adic automorphisms of the p-ary rooted tree. The groups are modeled after the first Grigorchuk group,…

Application of Computational Tools for Finitely Presented Groups

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Under suitable circumstances a finitely presented group can be shown to be soluble and its complete derived series can be determined, using what is in effect a soluble quotient algorithm.

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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…

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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…

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A number of significant applications of the low-index subgroups procedure are discussed, in particular to the construction of graphs and surfaces with large automorphism groups and three useful adaptations of the procedure are described.

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We study the subgroup structure, Hecke algebras, quasi-regular representations, and asymptotic properties of some fractal groups of branch type. We introduce parabolic subgroups, show that they are…