Unions of slender groups

It is well-known that the class of slender groups is closed under extensions, arbitrary direct sums and subgroups. We show that it is also closed under taking unions of continuous well-ordered ascending chains of groups where each factor of consecutive groups is slender (Theorem 2.2). We also prove that the class of slender groups cannot be obtained from any set of slender groups by forming unions of chains of the mentioned kind and taking subgroups (Theorem 4.2). This generalizes a result by G?bel-Wald 11]. We observe that the same results hold if in the theorems ‘slender’ is replaced by ‘reduced torsion-free’ or ‘cotorsion-free’. Received: 30 June 2005