Faithful group actions and Schreier graphs

Author:

Fedorova M.

Abstract

Each action of a finitely generated group on a set uniquely defines a labelled directed graph called the Schreier graph of the action. Schreier graphs are used mainly as a tool to establish geometrical and dynamical properties of corresponding group actions. In particilar, they are widely used in order to check amenability of different classed of groups. In the present paper Schreier graphs are utilized to construct new examples of faithful actions of free products of groups. Using Schreier graphs of group actions a sufficient condition for a group action to be faithful is presented. This result is applied to finite automaton actions on spaces of words i.e. actions defined by finite automata over finite alphabets. It is shown how to construct new faithful automaton presentations of groups upon given such a presentation. As an example a new countable series of faithful finite automaton presentations of free products of finite groups is constructed. The obtained results can be regarded as another way to construct new faithful actions of  groups  as soon as at least one such an action is provided.

Publisher

Vasyl Stefanyk Precarpathian National University

Subject

General Mathematics

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Action graph of a semigroup act & its functorial connection;CATEG GEN ALGEBRAIC;2023

2. On Schreier graphs of gyrogroup actions;Journal of Pure and Applied Algebra;2022-12

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