# Generic properties in some classes of automaton groups

## TL;DR

This paper demonstrates that in several key classes of automaton groups generated by Mealy automata, almost all groups contain elements of infinite order, often implying exponential growth.

## Contribution

It establishes that for important classes of Mealy automata, almost all generated groups have elements of infinite order, revealing generic properties.

## Key findings

- Almost all groups in certain automaton classes have infinite order elements.
- In some cases, groups exhibit exponential growth.
- Results apply to various significant classes of Mealy automata.

## Abstract

We prove, for various important classes of Mealy automata, that almost all generated groups have an element of infinite order. In certain cases, it also implies other results such as exponential growth.