On the concept of fractality for groups of automorphisms of a regular rooted tree

Jone Uria-Albizuri

On the concept of fractality for groups of automorphisms of a regular rooted tree

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arxiv 1604.05950 v1 pith:ST5C5HUE submitted 2016-04-20 math.GR

Jone Uria-Albizuri This is my paper · ORCID

classification math.GR

keywords fractalityautomorphismsgroupregularrootedtreearticleclarify

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The aim of this article is to discuss and clarify the notion of fractality for subgroups of the group of automorphisms of a regular rooted tree. For this purpose we define three types of fractality. We show that they are not equivalent, by giving explicit examples. Furthermore we present some tools that are helpful in order to determine the fractality of a given group.

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Groups of finite type: classification and structural properties
math.GR 2025-09 conditional novelty 7.0 of 10

For many groups of finite type, topological finite generation, just-infiniteness and strong completeness are equivalent, and new algorithms classify the groups up to isomorphism on binary and ternary trees.

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