Geodesic
A Generalization of Final Rank of Primary Abelian Groups
Canadian journal of mathematics, Tome 22 (1970) no. 6, pp. 1118-1122

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

Let G be a p-primary Abelian group. Recall that the final rank of G is infn∈ω {r(pnG)}, where r(pnG) is the rank of pnG and ω is the first limit ordinal. Alternately, if Γ is the set of all basic subgroups of G, we may define the final rank of G by supB∈Γ {r(G/B)}. In fact, it is known that there exists a basic subgroup B of G such that r(G/B) is equal to the final rank of G. Since the final rank of G is equal to the final rank of a high subgroup of G plus the rank of pωG, one could obtain the same information if the definition of final rank were restricted to the class of p-primary Abelian groups of length ω. 
Cutler, Doyle O.; Dubois, Paul F. A Generalization of Final Rank of Primary Abelian Groups. Canadian journal of mathematics, Tome 22 (1970) no. 6, pp. 1118-1122. doi: 10.4153/CJM-1970-129-4
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