On λ-large subgroups of n-summable Cω1-groups

Abstract

For any ordinal $\omega \le \lambda \le {\omega }_1$ and any natural 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 Linton (Pac. J. Math., 1978) and a recent author’s result (Algebra Colloq., 2009) as well.