A new characterization for 𝑝-local balanced projective groups

Lane, Mark

doi:10.1090/S0002-9939-1986-0822423-1

A new characterization for $p$-local balanced projective groups
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Proc. Amer. Math. Soc. 96 (1986), 379-386 Request permission

Abstract:

By introducing the notion of a ${\text {K}}$-nice submodule, we obtain a characterization of $p$-local balanced projectives perfectly analogous to the familiar third axiom of countability characterization of totally projective $p$-groups. We use this new characterization to prove that if a $p$-local group $G$ satisfies the third axiom of countability with respect to nice submodules and has a ${\text {K}}$-basis, then $G$ is a balanced projective.

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