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 Fundam. Prikl. Mat., 2019, Volume 22, Issue 5, Pages 121–130 (Mi fpm1840)

On a class of quotient divisible Abelian groups with isomorphic endomorphism semigroups

O. V. Lyubimtsev

Lobachevski State University of Nizhni Novgorod

Abstract: Let $\Lambda$ be some class of Abelian groups. We say that a group $A\in\Lambda$ is determined by its endomorphism semigroup $E^\star(A)$ in $\Lambda$ if the isomorphism $E^\star(A)\cong E^\star(B)$, where $B\in\Lambda$, implies $A\cong B$. 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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UDC: 512.541

Citation: O. V. Lyubimtsev, “On a class of quotient divisible Abelian groups with isomorphic endomorphism semigroups”, Fundam. Prikl. Mat., 22:5 (2019), 121–130

Citation in format AMSBIB
\Bibitem{Lju19} \by O.~V.~Lyubimtsev \paper On a~class of quotient divisible Abelian groups with isomorphic endomorphism semigroups \jour Fundam. Prikl. Mat. \yr 2019 \vol 22 \issue 5 \pages 121--130 \mathnet{http://mi.mathnet.ru/fpm1840}