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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A new characterization for $p$-local balanced projective groups


Author: Mark Lane
Journal: Proc. Amer. Math. Soc. 96 (1986), 379-386
MSC: Primary 20K21; Secondary 20K10
DOI: https://doi.org/10.1090/S0002-9939-1986-0822423-1
MathSciNet review: 822423
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Abstract: By introducing the notion of a ${\text {K}}$-nice submodule, we obtain a characterization of $p$-local balanced projectives perfectly analogous to the familiar third axiom of countability characterization of totally projective $p$-groups. We use this new characterization to prove that if a $p$-local group $G$ satisfies the third axiom of countability with respect to nice submodules and has a ${\text {K}}$-basis, then $G$ is a balanced projective.


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Keywords: Balanced projective groups, <!– MATH ${\text {K}}$ –> <IMG WIDTH="21" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${\text {K}}$">-module, <!– MATH ${\text {K}}$ –> <IMG WIDTH="21" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img3.gif" ALT="${\text {K}}$">-nice, third axiom of countability, Ulm invariants, <IMG WIDTH="17" HEIGHT="19" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="$h$">-invariants
Article copyright: © Copyright 1986 American Mathematical Society