title: Homological properties of quotient divisible Abelian groups and compact groups dual to them
metadata.name: dc.contributor.author
metadata.value: Kryuchkov, Nikolay I.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-05-28T17:07:15Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-05-28T17:07:15Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Kryuchkov N. I. Homological properties of quotient divisible Abelian groups and compact groups dual to them. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 2, pp. 236–244.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2020.206
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/17936
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The paper is devoted to the study of homological properties of quotient divisible Abelian
  groups. These groups constitute an important class of groups that has been intensively studied
  in recent years. In the first part of the paper, we study the conditions for the vanishing
  of extension groups in which one of the arguments is a quotient divisible group. Under
  some additional assumptions, groups of homomorphisms from quotient divisible groups to reduced abelian groups are described. Some properties of the universality of quotient divisible
  Abelian groups are investigated. The second part of the work is devoted to the study
  of the homological properties of compact Abelian groups, which are dual in the sense of
  L. S. Pontryagin to quotient divisible groups. Such groups are called quotient toroidal. We
  study the conditions for the vanishing of extension groups in which one of the arguments is
  a quotient toroidal group. Some groups of continuous homomorphisms in which the second
  argument is a quotient toroidal group are described. In the last part of the paper, we study
  the conditions for the vanishing of extension groups of quotient divisible groups with the
  help of compact quotient toroidal ones. The fundamental group of the topological space of
  the quotient toroidal group is characterized.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 7 (65); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: quotient divisible abelian group
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: dual compact group
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: group of extensions
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: homotopic group
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: group of homomorphisms
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Homological properties of quotient divisible Abelian groups and compact groups dual to them
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 236-244.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/17936/1/236-244.pdf
resources.format: Adobe PDF
resources.size: 308,18 kB