Portrait growth in contracting, regular branch groups

Zoran Sunic; Jone Uria-Albizuri

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arXiv · 1710.02902

Portrait growth in contracting, regular branch groups

Zoran Sunic·Jone Uria-Albizuri

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Abstract

We address a question of Grigorchuk by providing both a system of recursive formulas and an asymptotic result for the portrait growth of the first Grigorchuk group. The results are obtained through analysis of some features of the branching subgroup structure of the group. More generally, we provide recursive formulas for the portrait growth of any finitely generated, contracting, regular branch group, based on the coset decomposition of the groups that are higher in the branching subgroup structure in terms of the lower subgroups. Using the same general approach we fully describe the portrait growth for all non-symmetric GGS-groups and for the Apollonian group.

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Zoran Sunic, Jone Uria-Albizuri. 2017-10-09. Portrait growth in contracting, regular branch groups. https://arxiv.org/abs/1710.02902

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