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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Countable unions of totally projective groups
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by Paul Hill PDF
Trans. Amer. Math. Soc. 190 (1974), 385-391 Request permission

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
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • 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