Amenability of group actions characterized by configuration equations

Abstract

Extending a result by Rosenblatt and Willis, we present a new characterization for amenability of group actions. We show that a group action is amenable if and only if certain linear equations admit normalized solutions. We also give a new statement for the ping-pong Lemma to ensure that the group action is nonamenable and then obtain an upper bound for its Tarski number. © 2024 Belgian Mathematical Society. All rights reserved.