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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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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Keywords: Primary abelian group, basic subgroups, high subgroups, automorphism group, equivalent subgroups
Article copyright: © Copyright 1970 American Mathematical Society