Isotype submodules of 𝑝-local balanced projective groups

Lane, Mark

doi:10.1090/S0002-9947-1987-0879576-4

Isotype submodules of $p$-local balanced projective groups

Author: Mark Lane
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
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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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