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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Last modified: May 23, 2007