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Proceedings of the American Mathematical Society

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

 
 

 

Primary abelian groups having all high subgroups isomorphic


Author: Doyle O. Cutler
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0627671-7
Keywords: High subgroup
Article copyright: © Copyright 1981 American Mathematical Society

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