Vol. 27, No. 3, 1968

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Thin abelian p-groups

Fred Richman

Vol. 27 (1968), No. 3, 599–606

An abelian p-group G is thin if every map from a torsion complete group to G is small. The class of thin groups is shown to be closed under arbitrary direct sums and extensions and hence any direct sum of countable reduced p-groups is thin. An example shows that, unlike for groups with no elements of infinite height, a reduced group may contain no unbounded torsion complete subgroups and still fail to be thin. Finally, these groups are used to settle questions in a certain relative homological algebra.

Mathematical Subject Classification
Primary: 20.30
Received: 21 September 1967
Published: 1 December 1968
Fred Richman