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- W4366974842 abstract "For an Abelian group G, any homomorphism $$mu :Gotimes Grightarrow G$$ is called a multiplication on G. The set $$text {Mult},G$$ of all multiplications on an Abelian group G itself is an Abelian group with respect to addition; the group is called the multiplication group of G. Let $${mathcal {A}}_0$$ be the class of all reduced block-rigid almost completely decomposable groups of ring type with cyclic regulator quotient. In this paper, for groups $$Gin {mathcal {A}}_0$$ , we describe groups $$text {Mult},G$$ . We prove that for $$Gin {mathcal {A}}_0$$ , the group $$text {Mult},G$$ also belongs to the class $${mathcal {A}}_0$$ . For any group $$Gin {mathcal {A}}_0$$ , we describe the rank, the regulator, the regulator index, invariants of near-isomorphism, a main decomposition, and a standard representation of the group $$text {Mult},G$$ ." @default.
- W4366974842 created "2023-04-27" @default.
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- W4366974842 date "2023-04-24" @default.
- W4366974842 modified "2023-10-17" @default.
- W4366974842 title "Multiplication Groups of Abelian Torsion-Free Groups of Finite Rank" @default.
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- W4366974842 doi "https://doi.org/10.1007/s00009-022-02255-4" @default.
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