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Homological properties of quotient divisible Abelian groups and compact groups dual to them
- Source :
- Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy. 7:236-244
- Publication Year :
- 2020
- Publisher :
- Saint Petersburg State University, 2020.
-
Abstract
- Homological properties of quotient divisible Abelian groups are studied. These groups form an important class of groups, which has been extensively studied in recent years. The first part of the paper is devoted to conditions for the triviality of extension groups in which one of the arguments is a quotient divisible group. Under certain additional assumptions, groups of homomorphisms from quotient divisible groups to reduced Abelian groups are described. Universality properties of quotient divisible Abelian groups are investigated. The second part of the paper considers homological properties of compact Abelian groups dual to quotient divisible groups in the sense of L.S. Pontryagin. Such groups are said to be “quotient toroidal.” Conditions for the triviality of group extensions in which one of the arguments is a quotient toroidal group are studied. Certain groups of continuous homomorphisms in which the second argument is a quotient toroidal group are described. The last part of the paper is devoted to conditions for the triviality of the groups of extensions of quotient divisible groups by compact quotient toroidal ones. The fundamental group of the topological space of a quotient toroidal group is characterized.
- Subjects :
- Pure mathematics
Fundamental group
General Mathematics
010102 general mathematics
General Physics and Astronomy
Topological space
01 natural sciences
Triviality
Divisible group
010305 fluids & plasmas
Universality (dynamical systems)
0103 physical sciences
Homomorphism
0101 mathematics
Abelian group
Quotient
Mathematics
Subjects
Details
- ISSN :
- 25875884 and 10253106
- Volume :
- 7
- Database :
- OpenAIRE
- Journal :
- Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
- Accession number :
- edsair.doi...........365e2e95ebf92ff22f81c7589612b716