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On the structure of abelian $ p$-groups


Author: Paul Hill
Journal: Trans. Amer. Math. Soc. 288 (1985), 505-525
MSC: Primary 20K10; Secondary 20K27
DOI: https://doi.org/10.1090/S0002-9947-1985-0776390-3
MathSciNet review: 776390
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Abstract: A new kind of abelian $ p$-group, called an $ A$-group, is introduced. This class contains the totally projective groups and Warfield's $ S$-groups as special cases. It also contains the $ N$-groups recently classified by the author. These more general groups are classified by cardinal (numerical) invariants which include, but are not limited to, the Ulm-Kaplansky invariants. Thus the existing theory, as well as the classification, of certain abelian $ p$-groups is once again generalized.

Having classified $ A$-groups (by means of a uniqueness and corresponding existence theorem) we can successfully study their structure and special properties. Such a study is initiated in the last section of the paper.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1985-0776390-3
Keywords: Totally projective group, $ S$-groups, isotype subgroup, extending isomorphisms, invariants, uniqueness and existence theorems, classification of abelian $ p$-groups
Article copyright: © Copyright 1985 American Mathematical Society

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