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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
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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  • [1] Haya Freedman, The automorphisms of countable primary reduced Abelian groups, Proc. London Math. Soc. (3) 12 (1962), 77–99. MR 0133381
  • [2] L. Fuchs, Abelian groups, International Series of Monographs on Pure and Applied Mathematics, Pergamon Press, New York-Oxford-London-Paris, 1960. MR 0111783
  • [3] P. Hill, Enumeration of subgroups of small abelian groups, (to appear).
  • [4] Irving Kaplansky, Infinite abelian groups, University of Michigan Press, Ann Arbor, 1954. MR 0065561
  • [5] H. Leptin, Zur Theorie der überabzählbaren abelschen 𝑝-Gruppen, Abh. Math. Sem. Univ. Hamburg 24 (1960), 79–90 (German). MR 0122875
  • [6] Charles K. Megibben, On mixed groups of torsion-free rank one, Illinois J. Math. 11 (1967), 134–144. MR 0202832
  • [7] Kenjiro Shoda, Über die Automorphismen einer endlichen Abelschen Gruppe, Math. Ann. 100 (1928), no. 1, 674–686 (German). MR 1512510, 10.1007/BF01448871
  • [8] D. Tarwater, Orbits of basic subgroups of primary abelian groups under automorphisms, (to appear).

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