Isotype knice subgroups of global Warfield groups

If H is an isotype knice subgroup of a global Warfield group G, we introduce the notion of a k-subgroup to obtain various necessary and sufficient conditions on the quotient group G/H in order for H itself to be a global Warfield group. Our main theorem is that H is a global Warfield group if and only if G/H possesses an H(ℵ₀)-family of almost strongly separable k-subgroups. By an H(ℵ₀)-family we mean an Axiom 3 family in the strong sense of P. Hill. As a corollary to the main theorem, we are able to characterize those global k-groups of sequentially pure projective dimension ⩽ 1.