Vol. 29, No. 1, 1969

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ISSN: 0030-8730
Primary Abelian groups modulo finite groups

Ronald J. Ensey

Vol. 29 (1969), No. 1, 77–81

Let 𝒜 be the category of Abelian groups, the Serre class of finite Abelian groups, and form the quotient category 𝒜. The purpose of this paper is to find a complete set of invariants for direct sums of countable reduced p-groups, such groups being considered as objects of the category 𝒜. Specifically, it will be shown that two direct sums of countable reduced p-groups G and H are isomorphic in 𝒜if and only if

fG(α) = fH(α) for almost all ordinal numbers α,


fG(α) ⁄= fH(α) implies max (fG (α ),fH (α )) < ℵ0.

Mathematical Subject Classification
Primary: 20.30
Received: 8 January 1968
Published: 1 April 1969
Ronald J. Ensey