New criteria for freeness in abelian groups. II

Hill, Paul

doi:10.1090/S0002-9947-1974-0352294-8

New criteria for freeness in abelian groups. II
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by Paul Hill

Trans. Amer. Math. Soc. 196 (1974), 191-201

DOI: https://doi.org/10.1090/S0002-9947-1974-0352294-8

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Abstract:

A new criterion is established for an abelian group to be free. The criterion is in terms of an ascending chain of free subgroups and is dependent upon a new class of torsion-free groups. The result leads to the construction, for each positive integer n, of a group ${G_n}$ of cardinality ${\aleph _n}$ that is not free but is ${\aleph _n}$-free. A conjecture in infinitary logic concerning free abelian groups is also verified.

References

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