On extensions of primary almost totally projective Abelian groups. (English) Zbl 1170.20310

Danchev, Peter V.

Math. Bohem. 133, No. 2, 149-155 (2008).

Summary: Suppose \(G\) is a subgroup of the reduced Abelian \(p\)-group \(A\). The following two dual results are proved: (*) If \(A/G\) is countable and \(G\) is an almost totally projective group, then \(A\) is an almost totally projective group. (**) If \(G\) is countable and nice in \(A\) such that \(A/G\) is an almost totally projective group, then \(A\) is an almost totally projective group.
These results somewhat strengthen theorems due to K. D. Wallace [J. Algebra 17, 482-488 (1971; Zbl 0215.39902)] and P. Hill [Commentat. Math. Univ. Carol. 36, No. 4, 795-804 (1995; Zbl 0845.20038)], respectively.

MSC:

20K10	Torsion groups, primary groups and generalized primary groups
20K27	Subgroups of abelian groups
20K35	Extensions of abelian groups

Keywords:

almost totally projective groups; countable Abelian \(p\)-groups; extensions

Citations:

Zbl 0215.39902; Zbl 0845.20038