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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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Isotype submodules of $p$-local balanced projective groups
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by Mark Lane PDF
Trans. Amer. Math. Soc. 301 (1987), 313-325 Request permission

Abstract:

By giving necessary and sufficient conditions for two isotype submodules of a $p$-local balanced projective group to be equivalent, we are able to introduce a general theory of isotype submodules of $p$-local balanced projective groups (or $IB$ modules). Numerous applications of the above result are available particularly for the special class of $IB$ modules introduced by Wick (known as SKT modules). We first show that the class of SKT modules is closed under direct summands, and then we are able to show that if $H$ appears as an isotype submodule of the $p$-local balanced projective group $G$ such that $G/H$ is the coproduct of countably generated torsion groups, then $H$ is an SKT module. Finally we show that $IB$ modules satisfy general structural properties such as transitivity, full transitivity, and the equivalence of ${p^\alpha }$-high submodules.
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 301 (1987), 313-325
  • MSC: Primary 20K21
  • DOI: https://doi.org/10.1090/S0002-9947-1987-0879576-4
  • MathSciNet review: 879576