Amenability of groups and semigroups characterized by Configuration

TL;DR

This paper introduces a new concept of amenability for groups and semigroups that encompasses existing notions like amenability and inner-amenability, and explores their properties and relations with configurations.

Contribution

It defines a novel form of amenability for groups and semigroups, extending previous concepts and linking them to configurations.

Findings

Introduces a new amenability concept for groups and semigroups.

Shows the relationship between the new concept and existing amenability notions.

Provides results connecting this concept with configurations.

Abstract

In 2005, Abdollahi and Rejali, studied the relations between paradoxical decompositions and configurations for semigroups. In the present paper, we introduce another concept of amenability on semigroups and groups which includes amenability of semigroups and inner-amenability of groups. We have the previous known results to semigroups and groups satisfying this concept.