L-presentations and branch groups
arXiv:math/0007062 · doi:10.1016/S0021-8693(03)00268-0
Abstract
We introduce L-presentations: group presentations given by a generating set, a set of relations and a set of substitution rules on the generating set producing more relations. We first study in full generality the structure of finitely L-presented groups, i.e. groups for which all the above sets are finite, and then show that a broad class of groups acting on rooted trees admit explicitly constructible finite L-presentations: they are the "branch" groups defined by R. Grigorchuk.
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Cited by in corpus (24)
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- A nilpotent quotient algorithm for L-presented groups
- Approximating the Schur multiplier of certain infinitely presented groups via nilpotent quotients
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- Profinite completion of Grigorchuk's group is not finitely presented
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- A Reidemeister-Schreier theorem for finitely -presented groups
- On the wgsc and qsf tameness conditions for finitely presented groups