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Notes on \(\lambda\)-large subgroups of primary Abelian groups and free valuated vector spaces. (English) Zbl 1163.20034

Let \(A\) be a \(C_\Omega\)-group. The author proves: (i) \(A\) is summable if and only if \(p^\alpha A\) is summable for some ordinal \(\alpha<\Omega\); and (ii) if \(L\) is a \(\lambda\)-large subgroup for some \(\lambda\) such that \(\omega\leq\lambda\leq\Omega\), then \(A\) is summable if and only if \(L\) is summable.
The second result extends a result of R. C. Linton [Pac. J. Math. 75, 477-485 (1978; Zbl 0392.20035)] and an earlier result of the author.

MSC:

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

Citations:

Zbl 0392.20035
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