Abstract:
Let $C $ be an Abelian group. A class $X $ of Abelian groups is called
a $_CE ^\bullet H $-class if for any groups $A,B \in X$,
it follows from the existence of isomorphisms
$E^\bullet (A) \cong E^\bullet (B)$ and
$\operatorname{Hom}(C,A)\cong \operatorname{Hom}(C,B) $
that there is an isomorphism $A\cong B $. In this paper,
conditions are studied under which the class $\Im _{\mathrm{cd}}^{\mathrm{ad}}$
of completely decomposable almost divisible Abelian groups
and class $ \Im _{\mathrm{cd}}^{*} $ of completely decomposable
torsion-free Abelian groups $A$ where $\Omega(A)$ contains only
incomparable types are $_CE ^\bullet H $-classes,
where $C $ is a completely decomposable torsion-free Abelian group.
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