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Proceedings of the American Mathematical Society

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

 
 

 

Another summable $ C\sb{\Omega }$-group


Author: Doyle O. Cutler
Journal: Proc. Amer. Math. Soc. 26 (1970), 43-44
MSC: Primary 20.30
DOI: https://doi.org/10.1090/S0002-9939-1970-0262355-1
MathSciNet review: 0262355
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Abstract: An example is given of a $ p$-primary Abelian group $ G$ having the following properties: $ G$ is summable; the length of $ G$ is $ \Omega $; the $ \alpha $th Ulm invariant of $ G$ is one for all $ \alpha < \Omega $; if $ \alpha < \Omega $, any $ {p^\alpha }G$-high subgroup of $ G$ is countable; $ G/{p^\alpha }G$ is countable for all $ \alpha < \Omega $; and $ G$ is not $ {p^\beta }$-projective for any ordinal $ \beta $.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0262355-1
Keywords: Summable, $ p$-primary Abelian group, length $ \Omega $, not $ {p^\beta }$-projective
Article copyright: © Copyright 1970 American Mathematical Society

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