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Pure N-high Subgroups, P-adic Topology and Direct Sums of Cyclic Groups

Published online by Cambridge University Press:  20 November 2018

Khalid Benabdallah  and
John Irwin
Khalid Benabdallah
Affiliation:
Université de Montréal, Montréal, Québec
John Irwin
Affiliation:
Wayne State University, Detroit, Michigan
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This paper is divided into two sections. In the first, we characterize the subgroups N of a reduced abelian primary group for which all pure N-high subgroups are bounded. This condition on pure N-high subgroups occurs in several instances, for instance, all pure N-high subgroups of a primary group G are bounded if G is the smallest pure subgroup of G containing N; all N-high subgroups are bounded if N ≠ 0 and all N-high subgroups are closed in the p-adic topology.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 2 , April 1974 , pp. 322 - 327
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Benabdallah, Khalid and Irwin, John M., On N-high subgroups of abelian groups, Bull. Soc. Math. France 96 (1968), 337–346.Google Scholar
2. Benabdallah, Khalid and Irwin, John M., On quasi-essential subgroups of primary abelian groups, Can. J. Math. 22 (1970), 1176–1184.Google Scholar
3. Benabdallah, Khalid, Pure N-high subgroups of abelian groups (to appear in Can. Math. Bull.).Google Scholar
4. Dieudonné, Jean, Sur les groupes abéliens infinis, Portugal. Math. 11 (1952), 1–5.Google Scholar
5. Fuchs, Laszlo, Abelian groups (Publishing house of the Hungarian Academy of Science, Budapest, 1958).Google Scholar
6. Fuchs, Laszlo, Infinite abelian groups, vol. 1 (Academic Press, New York, 1970).Google Scholar
7. Irwin, John and O'Neil, John, On direct products of abelian groups, Can. J. Math. 22 (1970), 525–544.Google Scholar
8. Irwin, John and Walker, Elbert, On N-high subgroups of abelian groups, Pacific J. Math. 2 (1961), 1363–1374.Google Scholar
9. Kaplansky, Irving, Infinite abelian groups (Univ. of Michigan Press, Ann Arbor, 1954).Google Scholar