Multiplications on torsion-free groups of finite rank
- Authors: Kompantseva E.I.1,2, Tuganbaev A.A.3
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Affiliations:
- Московский педагогический государственный университет
- Финансовый университет при Правительстве Российской Федерации
- Национальный исследовательский университет «МЭИ»
- Issue: Vol 219 (2023)
- Pages: 3-15
- Section: Статьи
- URL: https://journals.rcsi.science/2782-4438/article/view/270998
- DOI: https://doi.org/10.36535/0233-6723-2023-219-3-15
- ID: 270998
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Abstract
A multiplication on an Abelian group G is an arbitrary homomorphism μ: G ⊗ G → G. The set MultG of all multiplications on an Abelian group G is itself an Abelian group with respect to addition. In this paper, we discuss the multiplication groups of groups from the class A0 of all Abelian block-rigid, almost completely decomposable groups of ring type with cyclic regulatory factors. We show that for any group G from the class A0, the group MultG also belongs to this class. The rank, regulator, regulator index, almost isomorphism invariants, principal decomposition, and standard representation of the group MultG for G ∈ A0 are described.
About the authors
E. I. Kompantseva
Московский педагогический государственный университет; Финансовый университет при Правительстве Российской Федерации
Author for correspondence.
Email: kompantseva@yandex.ru
Russian Federation, Москва; Москва
A. A. Tuganbaev
Национальный исследовательский университет «МЭИ»
Email: tuganbaev@gmail.com
Russian Federation, Москва
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