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

Mekler, Alan H.

doi:10.1090/S0002-9947-1987-0896012-2

The structure of groups which are almost the direct sum of countable abelian groups
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by Alan H. Mekler

Trans. Amer. Math. Soc. 303 (1987), 145-160

DOI: https://doi.org/10.1090/S0002-9947-1987-0896012-2

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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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