Countable-configurations and paradoxical decompositions
Functional Analysis
2021-10-22 v1
Abstract
In this paper we define countable-configuration of groups and prove that two Hopfian groups with the same set of countable-configurations are isomorphic and vice versa. We also study the countable paradoxical decomposition of groups. It is proved that a group G admits a countable paradoxical decomposition if and only if it is infinite.
Cite
@article{arxiv.2110.10203,
title = {Countable-configurations and paradoxical decompositions},
author = {M. Meisami and A. Rejali and A. Yousofzadeh},
journal= {arXiv preprint arXiv:2110.10203},
year = {2021}
}