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An automata group of intermediate growth and exponential activity. (English) Zbl 1428.20031

The author exhibits a new automata group \(G\) with intermediate growth and exponential activity. The automaton generating this group is inspired by a construction due to Wilson of groups of non-uniform exponential growth. Recall that the activity function of an automorphism of a rooted tree counts the number of non-trivial sections at a given level. The limit space of \(G\) is not simply connected.

MSC:

20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
20E07 Subgroup theorems; subgroup growth
20E08 Groups acting on trees
20F69 Asymptotic properties of groups

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References:

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