Vol. 107, No. 2, 1983

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When Tor(A, B) is a direct sum of cyclic groups

Paul Daniel Hill

Vol. 107 (1983), No. 2, 383–392

Necessary conditions are given in order that Tor(A,B) be a direct sum of cyclic groups for abelian groups A and B. Sufficient conditions are also given that compare with the necessary conditions. They are only slightly stronger if at all, and the two are equivalent for groups of cardinality not exceeding 2.

Due to the complexity of the problem, these conditions are not absolute, but constitute a reduction to smaller cardinality. The results generalize earlier results of R. Nunke.

Mathematical Subject Classification 2000
Primary: 20K10
Secondary: 20K40
Received: 11 August 1981
Published: 1 August 1983
Paul Daniel Hill