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On definability of a periodic EndE+-group by its endomorphism group

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Let A be a class of Abelian groups, A ∈ A, and End(A) be the additive endomorphism group of the group A. The group A is said to be defined by its endomorphism group in the class {ie208-01} if for every group B ∈ B such that End(B) ≅ End(A) the isomorphism B ≅ A holds. The paper considers the problem of definability of a periodic Abelian group A such that End-End(A) ≅ End(A). The classes of periodical Abelian groups, of divisible Abelian groups, of reduced Abelian groups, of nonreduced Abelian groups, and of all Abelian groups are investigated in this paper.

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  1. Nizhny Novgorod State Pedagogical University, Nizhny Novgorod, Russia

    E. M. Kolenova

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  1. E. M. Kolenova
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Correspondence to E. M. Kolenova.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 2, pp. 123–131, 2007.

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Kolenova, E.M. On definability of a periodic EndE+-group by its endomorphism group. J Math Sci 154, 208–213 (2008). https://doi.org/10.1007/s10958-008-9159-3

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  • DOI: https://doi.org/10.1007/s10958-008-9159-3

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