Geodesic
On Direct Products of Abelian Groups
Canadian journal of mathematics, Tome 22 (1970) no. 3, pp. 525-544

Voir la notice de l'article provenant de la source Cambridge University Press

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[λG λ], 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. 
Irwin, John M.; O'Neill, John D. On Direct Products of Abelian Groups. Canadian journal of mathematics, Tome 22 (1970) no. 3, pp. 525-544. doi: 10.4153/CJM-1970-061-5
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