Skip to main content

Vanishing theorems for cohomology of locally nilpotent groups

  • Conference paper
  • First Online:
Group Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1281))

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 29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 39.99
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.W. Barnes, P. Schmid and U. Stammbach Cohomological characterizations of saturated formations and homomorphs of finite groups, Comment. Math. Helv. 53 (1978), 165–173.

    Article  MathSciNet  MATH  Google Scholar 

  2. N. Bourbaki Commutative Algebra, Addison-Wesley, Reading (1972).

    MATH  Google Scholar 

  3. K.S. Brown and E. Dror The Artin-Rees property and homology, Israel J. Math. 22 (1975), 93–109.

    Article  MathSciNet  MATH  Google Scholar 

  4. P.M. Curran Fixed-point-free actions on a class of abelian groups, Proc. Amer. Math. Soc. 57 (1976), 189–193.

    Article  MathSciNet  MATH  Google Scholar 

  5. W. Dwyer Vanishing homology over nilpotent groups, Proc. Amer. Math. Soc. 49 (1975), 8–12.

    Article  MathSciNet  MATH  Google Scholar 

  6. W. Gaschütz Zur Erweiterungstheorie der endlichen Gruppen, J. reine angew. Math. 190 (1952), 93–107.

    MathSciNet  MATH  Google Scholar 

  7. R. Goblot Sur les dériveś de certaines limites projectives. Application aux modules, Bull. Sci. Math. 94 (1970), 251–255.

    MathSciNet  MATH  Google Scholar 

  8. R.L. Griess Fixed point free action and vanishing cohomology, preprint.

    Google Scholar 

  9. A. Grothendieck Sur quelques points d'algèbre homologique, Tohoku Math. J. 9 (1957), 119–221.

    MathSciNet  MATH  Google Scholar 

  10. B. Hartley Splitting over the locally nilpotent residual for a class of locally finite groups, Quart. J. Math. (2) 27 (1976), 395–400.

    Article  MathSciNet  MATH  Google Scholar 

  11. B. Hartley and M.J. Tomkinson Splitting over nilpotent and hypercentral residuals, Math. Proc. Cambridge Philos. Soc. 78 (1975), 215–226.

    Article  MathSciNet  MATH  Google Scholar 

  12. P.J. Hilton and U. Stammbach A Course in Homological Algebra, Springer, New York (1970).

    MATH  Google Scholar 

  13. D.F. Holt On the cohomology of locally finite groups, Quart. J. Math. (2) 32 (1981), 165–172.

    Article  MathSciNet  MATH  Google Scholar 

  14. B. Huppert Endliche Gruppen I, Springer, Berlin (1979).

    MATH  Google Scholar 

  15. C.U. Jensen Les Foncteurs Dérivés de lim et leurs Application en Theorie des Modules, Lecture Notes in Mathematics, vol. 254, Springer, Berlin (1970).

    Google Scholar 

  16. D.J.S. Robinson On the cohomology of soluble groups of finite rank, J. Pure Appl. Algebra 6 (1975), 155–164.

    Article  MathSciNet  MATH  Google Scholar 

  17. ___ The vanishing of certain homology and cohomology groups, J. Pure Appl. Algebra 7 (1976), 145–167.

    Article  MathSciNet  MATH  Google Scholar 

  18. ___ Recent results on finite complete groups, Algebra, Carbondale 1980, pp. 178–185. Lecture Notes in Math. 848, Springer, Berlin (1981).

    Google Scholar 

  19. ___ Cohomology of locally nilpotent groups, to appear

    Google Scholar 

  20. J.-L. Roque Annulation des groupes nilpotents de type fini, C.R. Acad. Sci. Paris. Série A, 284 (1977), 1257–1260.

    MathSciNet  MATH  Google Scholar 

  21. E. Schenkman The splitting of certain solvable groups, Proc. Amer. Math. Soc. 6 (1955), 286–290.

    Article  MathSciNet  MATH  Google Scholar 

  22. D.I. Zaicev On extensions of abelian groups, Akad. Nauk Ukr. SSR, Inst. Mat. (1980), 16–40.

    Google Scholar 

  23. ___ Soluble extensions of abelian groups, Akad. Nauk Ukr. SSR Inst. Mat. (1981), 14–25.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Otto H. Kegel Federico Menegazzo Giovanni Zacher

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag

About this paper

Cite this paper

Robinson, D.J.S. (1987). Vanishing theorems for cohomology of locally nilpotent groups. In: Kegel, O.H., Menegazzo, F., Zacher, G. (eds) Group Theory. Lecture Notes in Mathematics, vol 1281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078698

Download citation

  • DOI: https://doi.org/10.1007/BFb0078698

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18399-0

  • Online ISBN: 978-3-540-47948-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics