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 | References | Similar Articles | Additional Information
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