L-presentations and branch groups

Details L-presentations and branch groups L-presentations and branch groups

2000-07-10

arxiv.org/abs/math/0007062v3

J. Algebra 268 (2003), no. 2, 419--443

Mathematics

Group Theory

Scientific paper

10.1016/S0021-8693(03)00268-0

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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