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Proceedings of the American Mathematical Society

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

 

 

Automorphisms of countable primary abelian groups


Author: Paul Hill
Journal: Proc. Amer. Math. Soc. 25 (1970), 135-140
MSC: Primary 20.30
DOI: https://doi.org/10.1090/S0002-9939-1970-0255674-6
MathSciNet review: 0255674
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Abstract: It is proved that the automorphism group $ A$ of a countable primary abelian group $ G$ is transitive on certain subsets of subgroups of $ G$. One such subset of subgroups in case $ G$ is without elements of infinite height is the collection of all basic subgroups of $ G$ with a fixed corank, finite or infinite.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0255674-6
Keywords: Primary abelian group, basic subgroups, high subgroups, automorphism group, equivalent subgroups
Article copyright: © Copyright 1970 American Mathematical Society