Intersections of pure subgroups in abelian groups
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- by D. Boyer and K. M. Rangaswamy PDF
- Proc. Amer. Math. Soc. 81 (1981), 178-180 Request permission
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
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Additional Information
- © Copyright 1981 American Mathematical Society
- 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