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On Direct Products of Abelian Groups

Published online by Cambridge University Press:  20 November 2018

John M. Irwin  and
John D. O'Neill
John M. Irwin
Affiliation:
Wayne State University, Detroit, Michigan
John D. O'Neill
Affiliation:
University of Detroit, Detroit, Michigan
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In this paper we investigate the properties of the product (or complete direct sum) of torsion Abelian groups. The chief results concern products of Abelian primary groups (p-groups). Given a set of p-groups, [Gλ], over an index set Λ, the product of these groups is written λλ∈ΔGλ, the torsion subgroup of the product of these p-groups is written T[λGλ], and the discrete direct sum of the p-groups is written Σ Gλ.

Definition. Σ Gλ is said to be an essentially bounded decomposition if and only if there exists an integer M > 0 such that MGλ = 0 for all but a finite number of Gλs; otherwise the decomposition is essentially unbounded.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 3 , 01 June 1970 , pp. 525 - 544
Copyright
Copyright © Canadian Mathematical Society 1970

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