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Title: Homomorphisms of Rank-1 Quotient Divisible Groups

Abstract

Torsion-free quotient divisible groups were introduced by R. Beaumont and R. Pierce in 1961. In 1998, A. A. Fomin and W. Wickless defined quotient divisible mixed groups and proved that categories of mixed quotient divisible groups and finite-rank torsion-free groups with quasihomomorphisms as morphisms are dual. In studying finite-rank torsion-free groups, rank-1 torsion-free groups play an important role, as many problems that are being solved in this class arise from them. This paper is devoted to the study of the homomorphism groups of rank-1 quotient divisible groups. The main achieved result is a full description of the homomorphism group in the language of characteristics.

Authors:
 [1]
  1. Moscow State Pedagogical University (Russian Federation)
Publication Date:
OSTI Identifier:
22771356
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Sciences
Additional Journal Information:
Journal Volume: 230; Journal Issue: 3; Conference: 5. All-Russian symposium on abelian groups, Biysk (Russian Federation), 20-25 Aug 2012; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; GROUP THEORY; RINGS; TORSION

Citation Formats

Davydova, O. I., E-mail: davydovaoi@yandex.ru. Homomorphisms of Rank-1 Quotient Divisible Groups. United States: N. p., 2018. Web. doi:10.1007/S10958-018-3744-X.
Davydova, O. I., E-mail: davydovaoi@yandex.ru. Homomorphisms of Rank-1 Quotient Divisible Groups. United States. doi:10.1007/S10958-018-3744-X.
Davydova, O. I., E-mail: davydovaoi@yandex.ru. Sun . "Homomorphisms of Rank-1 Quotient Divisible Groups". United States. doi:10.1007/S10958-018-3744-X.
@article{osti_22771356,
title = {Homomorphisms of Rank-1 Quotient Divisible Groups},
author = {Davydova, O. I., E-mail: davydovaoi@yandex.ru},
abstractNote = {Torsion-free quotient divisible groups were introduced by R. Beaumont and R. Pierce in 1961. In 1998, A. A. Fomin and W. Wickless defined quotient divisible mixed groups and proved that categories of mixed quotient divisible groups and finite-rank torsion-free groups with quasihomomorphisms as morphisms are dual. In studying finite-rank torsion-free groups, rank-1 torsion-free groups play an important role, as many problems that are being solved in this class arise from them. This paper is devoted to the study of the homomorphism groups of rank-1 quotient divisible groups. The main achieved result is a full description of the homomorphism group in the language of characteristics.},
doi = {10.1007/S10958-018-3744-X},
journal = {Journal of Mathematical Sciences},
issn = {1072-3374},
number = 3,
volume = 230,
place = {United States},
year = {2018},
month = {4}
}