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