Geodesic
Pure-complete subgroups of direct sums of Prüfer groups
Glasgow mathematical journal, Tome 13 (1972) no. 1, pp. 47-48

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

Suppose that G is a p-primary abelian group. The subgroup G[p] = {x∈G:px=0} is called the socle of G and any subgroup S of G[p] is called a subsocle of G. If each subsocle of G supports a pure subgroup, then G is said to be pure-complete [1]. It is well known that, if G a direct sum of cyclic groups, then G is necessarily pure-complete. Further results about pure-complete groups are contained in [1] and [3]. 
Hill, Paul. Pure-complete subgroups of direct sums of Prüfer groups. Glasgow mathematical journal, Tome 13 (1972) no. 1, pp. 47-48. doi: 10.1017/S0017089500001361
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[1] 1.Hill, P., Pure subgroups having prescribed socles, Bull. Amer. Math. Soc. 71 (1965), 608–609. Google Scholar | DOI

[2] 2.Hill, P., Primary groups with uncountably many elements of infinite height, Arch. Math. 19 (1968), 279–283. Google Scholar | DOI

[3] 3.Hill, P. and Megibben, C., On primary groups with countable basic subgroups, Trans. Amer. Math. Soc. 124 (1966), 49–59. Google Scholar | DOI

[4] 4.Hill, P. and Megibben, C., On direct sums of countable groups and generalizations, Studies on abelian groups (Springer-Verlag, 1968). Google Scholar

[5] 5.Megibben, C., Note on a paper of Bernard Charles, Bull. Math. Soc. France 91 (1963), 453–454. Google Scholar | DOI

[6] 6.Fuchs, L., Infinite abelian groups, Vol. 1 (London, 1970). Google Scholar

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