Generalized Torsion Complete Groups

John D. Waller
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John D. Waller: Institute for Defense Analyses

Chapter [23] in Études sur les Groupes abéliens / Studies on Abelian Groups, 1968, pp 345-356 from Springer

Abstract: Abstract It is veil known that the direct sums of countable groups and the torsion complete groups are determined up to isomorphism by their Ulm invariants. The latter type of groups can be characterized as the torsion subgroup of the completion of a direct sum of cyclic groups. This completion is taken with respect to a p-adic topology which is described in Kaplansky’s [3] book and is defined there only for groups without elements of infinite height. The purpose of this paper is to extend the definition of this topology to include groups of arbitrary countable length and to investigate the torsion complete concept in this case.

Keywords: Cauchy Sequence; Countable Group; Natural Topology; Torsion Subgroup; Dense Subgroup (search for similar items in EconPapers)
Date: 1968
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DOI: 10.1007/978-3-642-46146-0_23

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