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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

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