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Pure-complete subgroups of direct sums of Prüfer groups

Published online by Cambridge University Press:  18 May 2009

Paul Hill
Paul Hill
Affiliation:
Florida State University, Tallahassee, Florida 32306
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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].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 13 , Issue 1 , March 1972 , pp. 47 - 48
Copyright
Copyright © Glasgow Mathematical Journal Trust 1972

References

REFERENCES

1.Hill, P., Pure subgroups having prescribed socles, Bull. Amer. Math. Soc. 71 (1965), 608–609.CrossRefGoogle Scholar
2.Hill, P., Primary groups with uncountably many elements of infinite height, Arch. Math. 19 (1968), 279–283.CrossRefGoogle Scholar
3.Hill, P. and Megibben, C., On primary groups with countable basic subgroups, Trans. Amer. Math. Soc. 124 (1966), 49–59.CrossRefGoogle Scholar
4.Hill, P. and Megibben, C., On direct sums of countable groups and generalizations, Studies on abelian groups (Springer-Verlag, 1968).Google Scholar
5.Megibben, C., Note on a paper of Bernard Charles, Bull. Math. Soc. France 91 (1963), 453–454.CrossRefGoogle Scholar
6.Fuchs, L., Infinite abelian groups, Vol. 1 (London, 1970).Google Scholar