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Unreduced Generalized Endoprimal Abelian Groups

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Abstract

An endofunction on an Abelian group A is a fonction f: An → A such that φf (x1, …, xn) = f (φ(x1), …, φ(xn)) for all endomorphisms φ of group A and all n from ℕ. If each endofunction has the form \(f\left(x_{1}, \ldots, x_{n}\right)=\sum\nolimits_{i=1}^{n} \lambda_{i} x_{i}\) for some central endomorphisms λ1, …, λn of group A, then such a group is called generalized endoprimal (GE) group. In this paper, we find GE-groups in the class of nonreduced Abelian groups. In addition, results paper, we find GE-group in the class of nonreduced Abelian groups. In addition, results concerning connections of GE-groups with Abelian groups whose endomorphism rings are unique addition rings have been obtained.

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Authors and Affiliations

  1. Lobachevsky State University of Nizhny Novgorod, 23 Gagarin Ave., Nizhny Novgorod, 603950, Russia

    O. V. Ljubimtsev

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  1. O. V. Ljubimtsev
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Correspondence to O. V. Ljubimtsev.

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Russian Text © The Author(s), 2019, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, No. 11, pp. 32–38.

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Ljubimtsev, O.V. Unreduced Generalized Endoprimal Abelian Groups. Russ Math. 63, 28–33 (2019). https://doi.org/10.3103/S1066369X19110045

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  • DOI: https://doi.org/10.3103/S1066369X19110045

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