Abstract
A class 𝒳 of abelian p-groups is closed under ω1-bijective homomorphisms if whenever f: G → H is a homomorphism with countable kernel and cokernel, then G ∈ 𝒳 iff H ∈ 𝒳. For an ordinal α, we consider the smallest class with this property containing (a) the p α-bounded simply presented groups; (b) the p α-projective groups; (c) the subgroups of p α-bounded simply presented groups. This builds upon classical results of Nunke from [14] and [15]. Particular attention is paid to the separable groups in these classes.
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