Growth of groups with incompressible elements, I
Group Theory
2025-01-24 v3 Dynamical Systems
Abstract
We define the class of groups of bounded type from tile inflations. These tile inflations also determine some automata describing the groups. In the case when the automata are stationary, we show that if the set of incompressible elements of a group in this class is finite, then this group has subexponential growth with a bounded power in the exponent. Then we describe some examples with certain special structures of orbital graphs and give explicit ways to find the upper bounds for the growth functions of these groups.
Cite
@article{arxiv.2402.16238,
title = {Growth of groups with incompressible elements, I},
author = {Zheng Kuang},
journal= {arXiv preprint arXiv:2402.16238},
year = {2025}
}
Comments
Fixed the definition of statioinary automaton and the discussion of stationary case. Fixed the proof of the main theorem