Abstract
Let Λ be some class of Abelian groups. We say that a group A ∈ Λ is determined by its endomorphism semigroup E⋆(A) in Λ if the isomorphism E⋆(A) ≅ E⋆(B), where B ∈ Λ, implies A ≅ B. We describe split Abelian groups in the class \( {\mathcal{QD}}_{\mathrm{cd}} \) of completely decomposable quotient divisible Abelian groups determined by their endomorphism semigroups in the class \( {\mathcal{QD}}_{\mathrm{cd}} \).
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 22, No. 5, pp. 121–130, 2019.
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Lyubimtsev, O.V. On a Class of Quotient Divisible Abelian Groups with Isomorphic Endomorphism Semigroups. J Math Sci 259, 467–473 (2021). https://doi.org/10.1007/s10958-021-05636-4
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DOI: https://doi.org/10.1007/s10958-021-05636-4