Danchev, Peter V. Notes on \(\lambda\)-large subgroups of primary Abelian groups and free valuated vector spaces. (English) Zbl 1163.20034 Bull. Allahabad Math. Soc. 23, No. 1, 149-154 (2008). 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. Reviewer: Todor Mollov (Plovdiv) Cited in 1 ReviewCited in 2 Documents MSC: 20K10 Torsion groups, primary groups and generalized primary groups 20K27 Subgroups of abelian groups Keywords:primary Abelian groups; \(\lambda\)-large subgroups; \(C_\lambda\)-groups; summable groups; valuated vector spaces Citations:Zbl 0392.20035 PDFBibTeX XMLCite \textit{P. V. Danchev}, Bull. Allahabad Math. Soc. 23, No. 1, 149--154 (2008; Zbl 1163.20034) Full Text: EuDML