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Intersections of pure subgroups in abelian groups


Authors: D. Boyer and K. M. Rangaswamy
Journal: Proc. Amer. Math. Soc. 81 (1981), 178-180
MSC: Primary 20K27
DOI: https://doi.org/10.1090/S0002-9939-1981-0593451-4
MathSciNet review: 593451
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Abstract: It is shown that a subgroup $ H$ of an abelian group $ G$ is an intersection of pure subgroups of $ G$ if and only if, for all primes $ p$ and positive integers $ n$, $ {p^n}g \in H$ and $ {p^{n - 1}}g \notin H$ imply that there exists $ z \in G$ such that $ {p^n}z = 0$ and $ {p^{n - 1}}z \notin H$. This solves a problem posed by $ L$. Fuchs in [2] and [3].


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0593451-4
Keywords: Abelian group, pure subgroup
Article copyright: © Copyright 1981 American Mathematical Society