Skip to main content
SpringerLink
Log in

A generalized hopf formula for higher homology groups

  • Published:
Commentarii Mathematici Helvetici

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Auslander, M. andLyndon, R. C.,Commutator subgroups of free groups, Amer. J. Math.77 (1955), 929–931.

    Article  MathSciNet  Google Scholar 

  2. Blackburn, N.,Note on a theorem of Magnus, J. Austral. Math. Soc.,10 (1969), 469–474.

    MathSciNet  Google Scholar 

  3. Brown, K. S.. Cohomology of groups. Springer-Verlag, New York, Berlin and Heidelberg 1982.

    MATH  Google Scholar 

  4. Conrad, B.,Crossed n-fold extensions of groups, n-fold extensions of modules, and higher multipliers, J. Pure Appl. Algebra36 (1985), 225–235.

    Article  MathSciNet  Google Scholar 

  5. Eilbenberg, S. andMac Lane, S.,Cohomology theory in abstract groups, I, II, Ann. of Math. (2)48 (1947), 51–78 and 326–341.

    Article  MathSciNet  Google Scholar 

  6. Gruenberg, K. W., A permutation theoretic description of group cohomology (unpublished).

  7. Gupta, N. D., Laffey, T. J. andThomson, M. W.,On the higher relation modules of a finite group, J. Algebra59 (1979), 172–187.

    Article  MathSciNet  Google Scholar 

  8. Holt, D.,An interpretation of the cohomology groups H n (G, M), J. Algebra60 (1979), 307–318.

    Article  MathSciNet  Google Scholar 

  9. Hopf, H.,Fundamentalgruppe und zweite Bettische Gruppe, Comment. Math. Helv.14 (1942), 257–309.

    MathSciNet  Google Scholar 

  10. Huebschmann, J.,Crossed n-fold extensions of groups and cohomology, Comment. Math. Helv.55 (1980), 302–314.

    MathSciNet  Google Scholar 

  11. Mac Lane, S.,Historical Note, J. Algebra60 (1979), 319–320.

    Article  MathSciNet  Google Scholar 

  12. Magnus, W.,,On a theorem of Marshall Hall, Ann. of Math.40 (1939), 764–768.

    Article  MathSciNet  Google Scholar 

  13. Magnus, W., Karras, A. andSolitar, D.,Combinatorial group theory, Wiley-Interscience, New York and London 1966.

    MATH  Google Scholar 

  14. Neumann, H., Varieties of groups, Springer-Verlag, Berlin, Heidelberg and New York 1967.

    MATH  Google Scholar 

  15. Schur, I.,Ober die Darstellung der endlichen Gruppen durch gebrochene lineare Substitutionen, J. Reine Angew. Math.127 (1904), 20–50.

    Google Scholar 

  16. Shmel’kin, A. L.,Wreath products and varieties of groups, Izv. Akad. Nauk SSSR Ser. Mat.29 (1965), 149–170 (Russian).

    MathSciNet  Google Scholar 

  17. Gruenberg, K. W.,Resolutions by relations, J. London Math. Soc.35 (1960), 481–494.

    MathSciNet  Google Scholar 

  18. Rodicio, A.,Presentaciones libres y H 2n (G), Publ. Mat. Univ. Aut. Barcelona30 (1986), 77–82.

    MathSciNet  Google Scholar 

  19. Brown, R. andEllis, G.,Hopf formulae for the higher homology of a group, Bull. London Math. Soc. (to appear).

Download references

Author information

Authors and Affiliations

  1. Karl-Weierstraß-Institut für Mathematik, Akademie der Wissenschaften der DDR, Mohrenstr. 39, DDR-1086, Berlin, German Democratic Republic

    Ralph Stöhr

Authors
  1. Ralph Stöhr
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stöhr, R. A generalized hopf formula for higher homology groups. Commentarii Mathematici Helvetici 64, 187–199 (1989). https://doi.org/10.1007/BF02564669

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02564669

Keywords

Search

Navigation