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.

Location: http://mech.math.msu.su/~fpm/eng/k07/k072/k07204h.htm

Last modified: May 23, 2007