Vol. 52, No. 1, 1974

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The uniqueness of elongations of Abelian groups

Robert Breckenridge Warfield, Jr.

Vol. 52 (1974), No. 1, 289–304

Given an Abelian group G and a functorial characteristic subgroup hG, we study the extent to which G is determined up to isomorphism by hG and GlhG. If G is a p-group or a mixed module over a discrete valuation ring, we study the structure of G in terms of that of pλG and G∕pλG, where λ is a limit ordinal. We also study a corresponding family of subgroups of Abelian groups in general. For a countably generated reduced module M of finite torsion-free rank over the ring Zp of integers localized at p, we obtain necessary and sufficient conditions for M to be determined up to isomorphism by pλM and M∕pλM.

Mathematical Subject Classification 2000
Primary: 20K10
Received: 11 September 1973
Published: 1 May 1974
Robert Breckenridge Warfield, Jr.