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On \(\lambda\)-large subgroups of \(n\)-summable \(C_{\omega_1}\)-groups. (English) Zbl 1158.20325

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.

MSC:

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