Abstract: | Let C be an Abelian group. An Abelian group A in some class
of Abelian groups is said to be
C
H-definable in the class
if, for any group B\in
, it follows from the existence of an isomorphism Hom(C,A) Hom(C,B) that there is an isomorphism A B. If every group in
is
C
H-definable in
, then the class
is called an
C
H-class. In the paper, conditions are studied under which a class of completely decomposable torsion-free Abelian groups is a
C
H-class, where C is a completely decomposable torsion-free Abelian group. |