Multiplication Groups of Abelian Torsion-Free Groups of Finite Rank

2022/05/21 by Е. И. Компанцева, Kompantseva, Ekaterina, A. A. Tuganbaev +1
Engineering · Mathematics · #16B99 #20K30 #20K99 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2205.10657

openalex publication_date 2022/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For an Abelian group G, any homomorphism μ\colon G⊗ G→ G is called a \textsfmultiplication on G. The set Mult G of all multiplications on an Abelian group G itself is an Abelian group with respect to addition; the group is called the \textsfmultiplication group of G. Let A₀ be the class of all reduced block-rigid almost completely decomposable groups of ring type with cyclic regulator quotient. In this paper, for groups G∈ A₀, we describe groups Mult G. We prove that for G∈ A₀, the group Mult G also belongs to the class A₀. For any group G∈ A₀, we describe the rank, the regulator, the regulator index, invariants of near-isomorphism, a main decomposition, and a standard representation of the group Mult G.

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