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arXiv · 1409.0125

On finite generation of self-similar groups of finite type

Ievgen V. Bondarenko·Igor O. Samoilovych
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Abstract

A self-similar group of finite type is the profinite group of all automorphisms of a regular rooted tree that locally around every vertex act as elements of a given finite group of allowed actions. We provide criteria for determining when a self-similar group of finite type is finite, level-transitive, or topologically finitely generated. Using these criteria and GAP computations we show that for the binary alphabet there is no infinite topologically finitely generated self-similar group given by patterns of depth $3$, and there are $32$ such groups for depth $4$.

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Ievgen V. Bondarenko, Igor O. Samoilovych. 2014-08-30. On finite generation of self-similar groups of finite type. https://arxiv.org/abs/1409.0125

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