Funny rank one and the approximate transitivity for induced actions
type: Item
instance of: scholarly article
title: Funny rank one and the approximate transitivity for induced actions
zbMATH Open document ID: 0947.46049
DOI: 10.1007/PL00010083
author: Alexandre M. Sokhet
published in: Monatshefte für Mathematik
publication date: 1999-09-22T00:00:00Z
review text: Let \(H\) be a closed normal subgroup of a locally compact separable group \(G\) acting ergodically on a Lebesgue space. It is proved, that if both the given \(H\)-section and the natural \(H\)-action on \(G/H\) have funny rank one, then the induced \(G\)-action has it too. A similar theorem is formulated for approximately transitive actions, even without the normality of \(H\). Corollaries concerning solvable group actions having discrete spectrum and fuzzy rank of a transitive action of a totally disconnected group are also provided.
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 28D15
Mathematics Subject Classification ID: 22F10
zbMATH DE Number: 1340544
zbMATH Keywords: ergodic theory
zbMATH Keywords: topological groups
zbMATH Keywords: appointment transitivity
zbMATH Keywords: funny rank one
zbMATH Keywords: approximately transitive actions
zbMATH Keywords: solvable group actions
zbMATH Keywords: discrete spectrum
zbMATH Keywords: totally disconnected group
reviewed by: Włodzimierz Ślęzak
MaRDI profile type: Publication
full work available at URL: pl00010083
OpenAlex ID: W2056983645
description: scientific article; zbMATH DE number 1340544