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Transactions of the American Mathematical Society

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

 
 

 

The structure of groups which are almost the direct sum of countable abelian groups


Author: Alan H. Mekler
Journal: Trans. Amer. Math. Soc. 303 (1987), 145-160
MSC: Primary 20K20; Secondary 03E35, 03E75, 20K25
DOI: https://doi.org/10.1090/S0002-9947-1987-0896012-2
MathSciNet review: 896012
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Abstract: The notion of being in standard form is defined for the groups described in the title of the paper which are of cardinality $ {\omega _1}$. Being in "standard form" is a structural description of the group. The consequences of being in standard form are explored, sometimes with the use of additional set-theoretic axioms. It is shown that it is consistent that a large class of these groups, including every weakly $ {\omega _1}$-separable $ {\omega _1}$-$ \Sigma $-cyclic group of cardinality $ {\omega _1}$, can be put in standard form.


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DOI: https://doi.org/10.1090/S0002-9947-1987-0896012-2
Article copyright: © Copyright 1987 American Mathematical Society

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