On the structure of primary abelian groups of countable Ulm type

Cutler, Doyle O.

doi:10.1090/S0002-9947-1970-0276330-9

On the structure of primary abelian groups of countable Ulm type
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by Doyle O. Cutler

Trans. Amer. Math. Soc. 152 (1970), 503-518

DOI: https://doi.org/10.1090/S0002-9947-1970-0276330-9

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Abstract:

In this paper we will give structure theorems for abelian $p$-groups of countable Ulm type utilizing the notion of high subgroup introduced by John M. Irwin and its generalization, $N$-high subgroup, introduced by Irwin and E. A. Walker. The general technique employed is to give conditions under which automorphisms of these subgroups extend to automorphisms of the group.

References

General topology

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Bernard Charles, Sous-groupes fonctoriels et topologies, Studies on Abelian Groups (Symposium, Montpellier, 1967) Springer, Berlin, 1968, pp. 75–92 (French). MR 0240195
Doyle O. Cutler and Robert W. Stringall, A topology for primary abelian groups, Studies on Abelian Groups (Symposium, Montpellier, 1967) Springer, Berlin, 1968, pp. 93–100. MR 0245671
L. Fuchs, Abelian groups, Publishing House of the Hungarian Academy of Sciences, Budapest, 1958. MR 0106942
Paul Hill and Charles Megibben, On primary groups with countable basic subgroups, Trans. Amer. Math. Soc. 124 (1966), 49–59. MR 199260, DOI 10.1090/S0002-9947-1966-0199260-9
John M. Irwin and Elbert A. Walker, On $N$-high subgroups of Abelian groups, Pacific J. Math. 11 (1961), 1363–1374. MR 136653
John M. Irwin and Elbert A. Walker, On $N$-high subgroups of Abelian groups, Pacific J. Math. 11 (1961), 1363–1374. MR 136653
J. M. Irwin and E. A. Walker, On isotype subgroups of Abelian groups, Bull. Soc. Math. France 89 (1961), 451–460. MR 147539
E. Kamke, Theory of Sets. Translated by Frederick Bagemihl, Dover Publications, Inc., New York, N.Y., 1950. MR 0032709
Irving Kaplansky, Infinite abelian groups, University of Michigan Press, Ann Arbor, 1954. MR 0065561
H. Leptin, Zur Theorie der überabzählbaren abelschen $p$-Gruppen, Abh. Math. Sem. Univ. Hamburg 24 (1960), 79–90 (German). MR 122875, DOI 10.1007/BF02942022