Abstract
Let \(\Lambda\) be a class of Abelian groups. A group \(A\in\Lambda\) is said to be determined by its endomorphism semigroup \(E^\star(A)\) in the class \(\Lambda\) if every isomorphism \(E^\star(A)\cong E^\star(B)\), where \(B\in\Lambda\), implies the isomorphism \(A\cong B\). The paper describes those Abelian groups in the class \(\mathscr Q\mathscr D_{\mathrm{cd}}\) of completely decomposable quotient divisible Abelian groups which are determined by their endomorphism semigroups in the class \(\mathscr Q\mathscr D_{\mathrm{cd}}\).
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This work was supported by government grant no. 0729-2020-0055.
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Lyubimtsev, O.V. Completely Decomposable Quotient Divisible Abelian Groups with Isomorphic Endomorphism Semigroups. Math Notes 108, 209–218 (2020). https://doi.org/10.1134/S0001434620070226
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DOI: https://doi.org/10.1134/S0001434620070226