Extensions of torsion-complete groups

Hill, Paul; Megibben, Charles

doi:10.1090/S0002-9939-1974-0340452-3

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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Extensions of torsion-complete groups
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by Paul Hill and Charles Megibben PDF

Proc. Amer. Math. Soc. 44 (1974), 259-262 Request permission

Abstract:

Problem 54 in L. Fuch’s Infinite abelian groups. Vol. II, is solved negatively. An abelian $p$-group without elements of infinite height can be an extension of one torsion-complete group by another without itself being torsion complete.

References

László Fuchs, Infinite abelian groups. Vol. II, Pure and Applied Mathematics. Vol. 36-II, Academic Press, New York-London, 1973. MR 0349869
Carl Peercy Walker, Properties of $\textrm {Ext}$ and quasi-splitting of Abelian groups, Acta Math. Acad. Sci. Hungar. 15 (1964), 157–160. MR 167526, DOI 10.1007/BF01897032