Danchev, Peter V. On \(\lambda\)-large subgroups of \(n\)-summable \(C_{\omega_1}\)-groups. (English) Zbl 1158.20325 SUT J. Math. 44, No. 1, 33-37 (2008). Summary: For any ordinal \(\omega\leq\lambda\leq\omega_1\) and any natural \(1\leq n<\omega\) we prove that a \(\lambda\)-large subgroup \(L\) of a primary \(C_{\omega_1}\)-group \(A\) is \(n\)-summable if and only if \(A\) is \(n\)-summable. This strengthens a classical result due to R. C. Linton [Pac. J. Math. 75, 477-485 (1978; Zbl 0392.20035)] and a recent result of the author’s [Algebra Colloq. 16, No. 4, 649-652 (2009; Zbl 1176.20055)] as well. Cited in 2 ReviewsCited in 2 Documents MSC: 20K10 Torsion groups, primary groups and generalized primary groups 20K27 Subgroups of abelian groups Keywords:fully invariant subgroups; large subgroups; summable groups; valuated vector spaces; totally projective groups Citations:Zbl 0392.20035; Zbl 1176.20055 PDFBibTeX XMLCite \textit{P. V. Danchev}, SUT J. Math. 44, No. 1, 33--37 (2008; Zbl 1158.20325)