On the structure of abelian $p$-groups
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- by Paul Hill PDF
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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.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- 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