What does this research mean for the field?

Every inner amenable transformation group constructed by the semidirect product of groups possesses property (W). Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

May 29, 2026Filomat0 citationsOpen Access

A menability and inner amenability of transformation groups

AEAli EbadianUrmia University AJAli JabbariKyrgyz-Türkish Manas Üniversity

Key Points

The aim is to explore the amenability and inner amenability of transformation groups derived from semidirect products.
Investigation of transformation groups formed through semidirect products
Introduction of the concept of inner amenability in this context
Characterization of inner amenable transformation groups
Every inner amenable transformation group demonstrates property (W).

Abstract

In this paper, we investigate the amenability of transformation groups constructed by the semidirect product of groups. We introduce the inner amenability of transformation groups and characterize this property. As an interesting result, we show that every inner amenable transformation group has property (W).

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