The balanced-projective dimension of abelian 𝑝-groups

Fuchs, L.; Hill, P.

doi:10.1090/S0002-9947-1986-0814915-0

The balanced-projective dimension of abelian $p$-groups
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Trans. Amer. Math. Soc. 293 (1986), 99-112 Request permission

Abstract:

The balanced-projective dimension of every abelian $p$-group is determined by means of a structural property that generalizes the third axiom of countability. As a corollary to our general structure theorem, we show for $\lambda = {\omega _n}$ that every ${p^\lambda }$-high subgroup of a $p$-group $G$ has balanced-projective dimension exactly $n$ whenever $G$ has cardinality ${\aleph _n}$ but ${p^\lambda }G \ne 0$. Our characterization of balanced-projective dimension also leads to new classes of groups where different infinite dimensions are distinguished.

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Cyclic purity: A generalization of purity to modules