Primary abelian groups having all high subgroups isomorphic
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- by Doyle O. Cutler PDF
- Proc. Amer. Math. Soc. 83 (1981), 467-470 Request permission
Abstract:
Let $G$ be a primary abelian group such that $G/{p^\omega }G$ is ${p^{\omega + n}}$-projective for some positive integer $n$, and if $n > 1$ then the $(\omega + m)$ Ulm invariant of $G$ is zero for $0 \leqslant m < n - 1$. We prove that $G$ has the property that all of its high subgroups are isomorphic. An example is given to show that in general the condition on the Ulm invariant is necessary and that this property is not preserved by direct sums.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 83 (1981), 467-470
- MSC: Primary 20K10
- DOI: https://doi.org/10.1090/S0002-9939-1981-0627671-7
- MathSciNet review: 627671