Vol. 52, No. 1, 1974

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Online Archive
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author index
To appear
Other MSP journals
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.