FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2007, VOLUME 13, NUMBER 2, PAGES 123-131

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

E. M. Kolenova

Abstract

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Let A be a class of Abelian groups, A Î 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 B Ê A if for every group B Î 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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