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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Automorphisms of countable primary abelian groups
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by Paul Hill
Proc. Amer. Math. Soc. 25 (1970), 135-140
DOI: https://doi.org/10.1090/S0002-9939-1970-0255674-6

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.
References
  • Haya Freedman, The automorphisms of countable primary reduced Abelian groups, Proc. London Math. Soc. (3) 12 (1962), 77–99. MR 133381, DOI 10.1112/plms/s3-12.1.77
  • L. Fuchs, Abelian groups, International Series of Monographs on Pure and Applied Mathematics, Pergamon Press, New York-Oxford-London-Paris, 1960. MR 0111783
  • P. Hill, Enumeration of subgroups of small abelian groups, (to appear).
  • Irving Kaplansky, Infinite abelian groups, University of Michigan Press, Ann Arbor, 1954. MR 0065561
  • H. Leptin, Zur Theorie der überabzählbaren abelschen $p$-Gruppen, Abh. Math. Sem. Univ. Hamburg 24 (1960), 79–90 (German). MR 122875, DOI 10.1007/BF02942022
  • Charles K. Megibben, On mixed groups of torsion-free rank one, Illinois J. Math. 11 (1967), 134–144. MR 202832
  • Kenjiro Shoda, Über die Automorphismen einer endlichen Abelschen Gruppe, Math. Ann. 100 (1928), no. 1, 674–686 (German). MR 1512510, DOI 10.1007/BF01448871
  • D. Tarwater, Orbits of basic subgroups of primary abelian groups under automorphisms, (to appear).
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Bibliographic Information
  • © Copyright 1970 American Mathematical Society
  • 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