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The third axiom of countability for Abelian groups. (English) Zbl 0467.20041


MSC:

20K10 Torsion groups, primary groups and generalized primary groups
20K27 Subgroups of abelian groups
20K15 Torsion-free groups, finite rank
20K20 Torsion-free groups, infinite rank
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[1] Peter Crawley and Alfred W. Hales, The structure of torsion abelian groups given by presentations, Bull. Amer. Math. Soc. 74 (1968), 954 – 956. · Zbl 0194.04502
[2] László Fuchs, Infinite abelian groups. Vol. II, Academic Press, New York-London, 1973. Pure and Applied Mathematics. Vol. 36-II. · Zbl 0257.20035
[3] Phillip A. Griffith, Infinite abelian group theory, The University of Chicago Press, Chicago, Ill.-London, 1970. · Zbl 0204.35001
[4] P. Hill, On the classification of abelian groups, xeroxed manuscript, 1967.
[5] Paul Hill, A countability condition for primary groups presented by relations of length two, Bull. Amer. Math. Soc. 75 (1969), 780 – 782. · Zbl 0192.35504
[6] Paul Hill, On the decomposition of certain infinite nilpotent groups, Math. Z. 113 (1970), 237 – 248. · Zbl 0175.29801
[7] R. J. Nunke, Homology and direct sums of countable abelian groups, Math. Z. 101 (1967), 182 – 212. · Zbl 0173.02401
[8] Elbert A. Walker, Ulm’s theorem for totally projective groups, Proc. Amer. Math. Soc. 37 (1973), 387 – 392. · Zbl 0257.20039
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