J Austral Math Soc Ser A 48 pp281--298, 1990.

Imbedded Subgroups of Abelian Groups

W. P. Berlinghoof, J. D. Moore and J. Reid

Abstract

A subgroup H of an abelian p-group G is pure in G if the inclusion map of H into G is an isometry with respect to the (pseudo-) metrics on H and G associated with their p-adic topologies. In this paper, those subgroups (called here imbedde subgroups) of abelian groups for which the inclusionis a homeomorphism with respect to the p-adic topologies are studies, the aim being to compare the concepts of imbeddedness and purity, Perhaps the main results indicate that imbedded subgroups are considerably more abundant than pure subgroup. Groups for which this is not the case are characterized.

1980 AMS Subject Classification (1985 Revision): 20K10

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Authors

W. P. Berlinghoff

Colby College, Waterville, Maine 04901, U.S.A.

J. D. Moore

Arizona State University, Temple, Arizona 85287, U.S.A.

J. D. Reid

Wesleyan University, Middletown, Connecticut 06457, U.S.A.