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L-presentations and branch groups

Laurent Bartholdi
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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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Laurent Bartholdi. 2000-07-10. L-presentations and branch groups. https://doi.org/10.1016/s0021-8693(03)00268-0

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