Automata generating free products of groups of order 2

TL;DR

This paper introduces a family of automata that generate free products of cyclic groups of order 2, expanding understanding of automata groups acting on rooted binary trees.

Contribution

It presents a novel construction of automata with n states that produce free products of groups of order 2, a new method in automata group theory.

Findings

Automata with n states generate free products of cyclic groups of order 2.

Construction works for n > 3.

Automata act on rooted binary trees.

Abstract

We construct a family of automata with n states, n>3, acting on a rooted binary tree that generate the free products of cyclic groups of order 2.