Periodica Mathematica Hungarica

, Volume 69, Issue 1, pp 41–52 | Cite as

On the classification of abelian groups

  • Paul HillEmail author

Remark With the exception of this remark (and perhaps one or two typos), this paper is an identical copy of a manuscript written by the author in 1967–1968 but never published in which the third axiom of countability was introduced and totally projective groups were classified. There have been dozens of subsequent papers that cited this work as “to appear” as well as in the references of a book by L. Fuchs and one by P. Griffith. To the best of the author’s knowledge, there is only one copy of the original manuscript still in existence. Taking into account these facts together with the fact that the paper is largely due to the influence of Laszlo Fuchs, it seems appropriate to publish it now in his honor.

We should advise the reader that throughout the summation symbol denotes the direct sum.


One of the nicest structure theorems in mathematics concerns abelian groups. It is the one that classifies countable primary groups: two countable, reduced, primary groups are...


Abelian Group Cyclic Group Projective Group Primary Group Critical Number 
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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2014

Authors and Affiliations

  1. 1.Auburn UniversityAuburnUSA

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