Skip to main content
Log in

Abelian group extensions and the axiom of constructibility

  • Published:
Commentarii Mathematici Helvetici

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  • [B1]Baer, R.,The subgroup of the elements of finite order of an abelian group, Ann. Math.37 (1936), 766–781.

    Article  MathSciNet  MATH  Google Scholar 

  • [B2]Baer, R.,Die Torsionsuntergruppe einer abelschen Gruppe, Math. Ann.135 (1958), 219–234.

    Article  MathSciNet  MATH  Google Scholar 

  • [E1]Eklof, P.,Whitehead's problem is undecidable, The Amer. Math. Monthyl83 (1976), 775–788.

    Article  MathSciNet  MATH  Google Scholar 

  • [E2]Eklof, P.,Homological algebra and set theory, Trans. Amer. Math. Soc.227 (1977), 207–225.

    Article  MathSciNet  MATH  Google Scholar 

  • [E3]Eklof, P.,Applications of logic to the problem of splitting abelian groups. Logic Colloquium 76, North-Holland (1977), 287–299.

  • [F1]Fuchs, L.,Infinite Abelian Groups, Vol. I, Academic Press, New York 1970.

    MATH  Google Scholar 

  • [F2]Fuchs, L.,Infinite Abelian Groups, Vol. II, Academic Press, New York 1973.

    MATH  Google Scholar 

  • [Hi]Hill, P.,On the freeness of abelian groups a generalization of Pontryagin's theorem, Bull. Amer. Math. Soc.76 (1970), 1118–1120.

    Article  MathSciNet  MATH  Google Scholar 

  • [H-H-S]Hiller, H., Huber, M., andShelah, S.,The structure of Ext (A,Z)and V=L, Math. Z.162 (1978), 39–50.

    Article  MathSciNet  MATH  Google Scholar 

  • [Hu]Huber, M.,Sur les groupes abéliens de la forme Ext(A, G), C. R. Acad. Sc. Paris,285 (1977), Série A, 529–531.

    MATH  Google Scholar 

  • [J]Jensen, C., Les Foncteurs Dérivés de\(\bar R^n \) et leurs Applications en Théorie des Modules, Lecture Notes in Math.254, Springer-Verlag, 1972.

  • [M-V]Meijer, A. andViljoen, G.,A note on the extensions of the infinite cyclic group and realizable groups, Arch. Math.25 (1974), 113–120.

    Article  MathSciNet  MATH  Google Scholar 

  • [N1]Nunke, R.,Modules of extensions over Dedekind rings, Illinois J. Math.3 (1959), 222–241.

    MathSciNet  MATH  Google Scholar 

  • [N2]Nunke, R.,A note on abelian group extensions, Pacific J. Math.12 (1962), 1401–1403.

    Article  MathSciNet  MATH  Google Scholar 

  • [R]Rotman, J.,On a problem of Baer and a problem of Whitehead in abelian groups, Acta Math. Acad. Sci. Hungar.12 (1961), 245–254.

    Article  MATH  Google Scholar 

  • [Sh1]Shelah, S.,Infinite abelian groups—Whitehead problem and some constructions, Israel J. Math.18 (1974), 243–256.

    Article  MathSciNet  MATH  Google Scholar 

  • [Sh2]Shelah, S.,A compactness theorem for singular cardinals, free algebras Whitehead problem and transversals, Israel J. Math.21 (1975), 319–349.

    Article  MathSciNet  MATH  Google Scholar 

  • [Sh3]Shelah, S.,Compactness in singular cardinals revisted, preprint.

  • [Sz]Szele, T.,On the basic subgroups of abelian p-groups, Acta Math. Acad. Sci. Hungar.5 (1954), 129–141.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Research of the first author partially supported by NSF grant MCS76-12014.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Eklof, P.C., Huber, M. Abelian group extensions and the axiom of constructibility. Commentarii Mathematici Helvetici 54, 440–457 (1979). https://doi.org/10.1007/BF02566286

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02566286

Keywords

Navigation