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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A new characterization for $ p$-local balanced projective groups

Author: Mark Lane
Journal: Proc. Amer. Math. Soc. 96 (1986), 379-386
MSC: Primary 20K21; Secondary 20K10
MathSciNet review: 822423
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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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Keywords: Balanced projective groups, $ {\text{K}}$-module, $ {\text{K}}$-nice, third axiom of countability, Ulm invariants, $ h$-invariants
Article copyright: © Copyright 1986 American Mathematical Society