Properties of covers in the lattice of group topologies for nilpotent groups
type: Item
instance of: scholarly article
zbMATH Open document ID: 1284.22001
publication date: 2014-01-29T00:00:00Z
full work available at URL: http://www.math.md/publications/basm/issues/y2012-n3/11399/
Mathematics Subject Classification ID: 22A05
zbMATH DE Number: 6251556
zbMATH Keywords: nilpotent group
zbMATH Keywords: group topology
zbMATH Keywords: lattice of group topologies
zbMATH Keywords: unrefinable chains
zbMATH Keywords: coatom
zbMATH Keywords: infimum of group topologies
author: Vladimir Arnautov
MaRDI profile type: Publication
title: Properties of covers in the lattice of group topologies for nilpotent groups
published in: Buletinul Academiei de Științe a Republicii Moldova. Matematica
review text: The author constructs a nilpotent group and group topologies \(\mathcal T_1\) and \(\mathcal T_2\) on it such that between \(\mathcal T_1\) and \(\inf\{\mathcal T_1,\mathcal T_2\}\) there exists a chain of group topologies isomorphic to \(\mathbb Z\) as an ordered set. Related results on lattices of group topologies on a nilpotent group have been obtained in [the author, Bul. Acad. Ştiinţe Repub. Mold., Mat. 2010, No. 2(63), 3--19 (2010; Zbl 1204.22001)].
reviewed by: Mihail I. Ursul
description: scientific article; zbMATH DE number 6251556