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Transactions of the American Mathematical Society

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Countable unions of totally projective groups


Author: Paul Hill
Journal: Trans. Amer. Math. Soc. 190 (1974), 385-391
MSC: Primary 20K10
DOI: https://doi.org/10.1090/S0002-9947-1974-0338212-7
MathSciNet review: 0338212
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Abstract: Let the p-primary abelian group G be the set-theoretic union of a countable collection of isotype subgroups $ {H_n}$ of countable length. We prove that if $ {H_n}$ is totally projective for each n, then G must be totally projective. In particular, an ascending sequence of isotype and totally projective subgroups of countable length leads to a totally projective group. The result generalizes and complements a number of theorems appearing in various articles in the recent literature. Several applications of the main result are presented.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0338212-7
Keywords: Abelian p-groups, totally projective groups, isotype subgroups, ascending chain, Kulikov's criterion
Article copyright: © Copyright 1974 American Mathematical Society