Skip to main content

Extensions of Butler Groups

  • Chapter
Abelian Group Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1006))

Abstract

M. C. R. Butler [B] introduced a class R (called Butler groups) of torsion free Abelian groups of finite rank that is the closure of the class of subgroups of the rationals under finite direct sums, torsion free epimorphic images, and pure subgroups. (i.e., R is the smallest torsion free class that contains the rank-1 torsion free Abelian groups.)

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. Arnold, Finite Rank Torsion Free Abelian Groups and Rings, Lecture Notes 931, Springer-Verlag, Berlin (1982).

    Google Scholar 

  2. D. Arnold,, “Pure subgroups of finite rank completely decomposable groups”, Abelian Group Theory, Lecture Notes 874, Springer-Verlag, Berlin (1981), 1–31.

    Google Scholar 

  3. D. Arnold, , and C. Vinsonhaler, “Pure subgroups of finite rank completely decomposable groups, II ”, preprint.

    Google Scholar 

  4. M. C. R. Butler, “A class of torsion free Abelian groups of finite rank”, Proc.London Math. Soc. (3) 15 (1965), 680–698.

    Article  Google Scholar 

  5. L. Fuchs, Infinite Abelian Groups, vol. II, Academic Press, San Francisco (1970).

    Google Scholar 

  6. E. L. Lady, “A seminar on splitting rings for torsion free modules over Dedekind domains”, preprint.

    Google Scholar 

  7. S. MacLane, Homology, Springer-Verlag, New York (1970).

    Google Scholar 

  8. C. P. Walker, “Properties of Ext and quasi-splitting of Abelian groups”, Acta Math. 15 (1964), 157–160.

    Google Scholar 

  9. R. B. Warfield, “Extensions of torsion free Abelian groups of finite rank”, Arch. Math. vol. XXIII, (1972), 145–150.

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Giovannitti, A. (1983). Extensions of Butler Groups. In: Göbel, R., Lady, L., Mader, A. (eds) Abelian Group Theory. Lecture Notes in Mathematics, vol 1006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21560-9_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-21560-9_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12335-4

  • Online ISBN: 978-3-662-21560-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics