This article is cited in 3 papers

A theorem on direct expansions of Abelian groups

A. Yu. Soifer

V. I. Lenin Moscow Pedagogical Institute

Abstract: The following assertion is proved: if the basis subgroups of the periodic part $t(G)$ of a non-denumerable Abelian $G$.oup $G$ 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.

UDC: 519.4

Received: 19.06.1972

 English version: Mathematical Notes, 1973, 14:6, 1064–1067

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