Amenability and Inner Amenability of Transformation Groups

TL;DR

This paper explores amenability and inner amenability in transformation groups, introducing new characterizations and examining properties of groups formed via semidirect products.

Contribution

It introduces the concept of inner amenability for transformation groups and provides characterizations, extending the understanding of amenability in complex group structures.

Findings

Existence of a net for amenable transformation groups similar to F{\

Inner amenability characterized for transformation groups

Analysis of amenability in semidirect product groups

Abstract

In this paper, we show that there is a net for amenable transformation groups like F{\o}lner net for amenable groups and investigate amenability of a transformation group constructed by semidirect product of groups. We introduce inner amenability of transformation groups and characterize this property.