Unions of slender groups. (Q2502312)

Given any smooth ascending chain of slender Abelian groups \(A_\alpha\), \(\alpha<\tau\), such that every \(A_{\alpha+1}/A_\alpha\) is slender, the authors prove that its union \(\bigcup A_\alpha\) is likewise slender. As customary the result holds up to the usual (non-)stationarity conditions. To prove this result, the authors resort to the old results of Nunke and/or Chase. An auxiliary result in the paper is that the whole class of slender groups cannot be generated from any \textbf{set} \(\mathcal M\) of slender groups by taking subgroups and unions of well-ordered ascending chains with consecutive factors in \(\mathcal M\).