A theorem on direct expansions of Abelian groups

The following assertion is proved: if the basis subgroups of the periodic part t(G) of a non-denumerable Abelian group G have the same cardinality as G, then each of the subgroups contains, as a subgroup of the same cardinality as G, a direct component of G. The restriction on the cardinality of G is essential.Translated from Matematicheskie Zametki, Vol. 14, No. 6, pp. 879–884, December, 1973.