Skip to main content

Integral representations and presentations of finite groups

  • Chapter
  • First Online:
Integral Representations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 744))

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

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
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. Baumslag, G.-D. Solitar, Some two-generator one-relator non-Hopfian groups, Bull. Amer. Math. Soc. 68, 199–201, 1962

    Article  MathSciNet  MATH  Google Scholar 

  2. Cossey, J.-K. W. Gruenberg-L. Kovacs, The presentation rank of a direct product of finite groups, J. Algebra 28, 597–603, 1974

    Article  MathSciNet  MATH  Google Scholar 

  3. Dade, E. C., Deux groupes finis distincts ayant la même algèbre de groupe sur tous corps, Math. Zeit. 119, 345–348, 1971

    Article  MathSciNet  MATH  Google Scholar 

  4. Dunwoody, M. J., Relation modules, Bull. London Math. Soc. 4, 151–155, 1972

    Article  MathSciNet  MATH  Google Scholar 

  5. Gaschütz, W., Zu einem von B. H. und H. Neumann gestellten Problem, Math. Nachrichten, 14, 249–252, 1955

    Article  MathSciNet  MATH  Google Scholar 

  6. Green, J. A., Blocks of modular representations, Math. Zeit. 79, 100–115, 1962

    Article  MathSciNet  MATH  Google Scholar 

  7. Gruenberg, K. W., Über Relationenmoduln einer endlichen Gruppe, Math. Zeit. 118, 30–33, 1970

    Article  MathSciNet  MATH  Google Scholar 

  8. Gruenberg, K. W., Groups of non-zero presentation rank, Symposia Math, 17, 215–224, 1976

    MathSciNet  MATH  Google Scholar 

  9. Gruenberg, K. W., Relation modules of finite groups, Regional conference series in Math., Amer. Math. Soc., 1976

    Google Scholar 

  10. Gruenberg, K. W.-K. W. Roggenkamp, Decomposition of the augmentation ideal and of the relation modules of a finite group, Proc. London Math. Soc. 31, 146–166, 1975

    MathSciNet  MATH  Google Scholar 

  11. Gruenberg, K. W.-K. W. Roggenkamp, Decomposition of the relation-modules of a finite group, J. London Math. Soc.(2), 12, 262–266, 1976

    Article  MathSciNet  MATH  Google Scholar 

  12. Gruenberg, K. W.-K. W. Roggenkamp, Projective covers for the augmentation ideals of finite groups, J. Pure App. Algebra 6, 165–176, 1975

    Article  MathSciNet  MATH  Google Scholar 

  13. Gruenberg, K. W.-K. W. Roggenkamp, Extension categories of groups and modules, I, II, to be published

    Google Scholar 

  14. Higman, G., The units of group rings, Proc. London Math. Soc. 46, 231–248, 1940

    Article  MathSciNet  MATH  Google Scholar 

  15. Huppert, B., Endliche Gruppen, Grundl. Math. Wiss. 134, Springer-verlag, Berlin, New York, 1971

    MATH  Google Scholar 

  16. Jacobinski, H., Genera and decomposition of lattices over orders, Acta Math. 121, 1–29, 1968

    Article  MathSciNet  MATH  Google Scholar 

  17. Kimmerle, W., Gruppenerweiterungen bezüglich einer Untergruppe, Diplomarbeit, Stuttgart, 1976

    Google Scholar 

  18. Kovács, L. G., On finite soluble groups, Math. Zeit. 103, 37–39, 1968

    Article  MathSciNet  MATH  Google Scholar 

  19. Miles, C. P., Aneis de grupos, Escola de Algebra, São Paulo, 1976

    MATH  Google Scholar 

  20. Pietsch, B., Gruppen-und Modulerweiterungen, Diplomarbeit, Bielefeld, 1975

    Google Scholar 

  21. Roggenkamp, K. W. Lattices over orders I, II Lecture Notes in Math. 115, 142, Springerverlag, Berlin, New York 1970

    MATH  Google Scholar 

  22. Roggenkamp, K. W., Relation modules of finite groups and related topics, Algebra i Logika 12, 351–359, 1973

    Article  MathSciNet  MATH  Google Scholar 

  23. Roggenkamp, K. W., Integral group rings of solvable finite groups have no idempotent ideals, Archiv Math. 25, 125–128, 1974

    Article  MathSciNet  MATH  Google Scholar 

  24. Roiter, A. V., On integral representations belonging to one genus, Izv. Akad. Nauk SSSR Ser. Mat. 30, 1315–1324, 1966

    MathSciNet  Google Scholar 

  25. Sehgal, S. K., On the isomorphism of integral group rings I, II, Can. J. Math. 21, 410–413; 1182–1188, 1969

    Article  MathSciNet  MATH  Google Scholar 

  26. Swan, R. G., Induced representations and projective modules, Ann. Math. (2) 71, 552–578, 1960

    Article  MathSciNet  MATH  Google Scholar 

  27. Swan, R. G., Minimal resolutions for finite groups, Topology 4, 193–208, 1965

    Article  MathSciNet  MATH  Google Scholar 

  28. Swan. R. G., K-theory for finite groups and orders, Lecture Notes in Math. 149, Springerverlag, Berlin, New York, 1970

    Book  MATH  Google Scholar 

  29. Wiegold, J., Growth sequences of finite groups, II, J. Austral. Math. Soc. 20, 225–229, 1975

    Article  MathSciNet  MATH  Google Scholar 

  30. Williams, J. S., Free presentations and relation modules of finite groups, J. Pure App. Algebra 3, 203–217, 1973

    Article  MathSciNet  MATH  Google Scholar 

  31. Williams, J. S., Projective objects in categories of group extensions, J. Pure App. Algebra 3, 375–383, 1973

    Article  MathSciNet  MATH  Google Scholar 

  32. Williams, J. S., Free objects in relative extension categories, unpublished, 1973

    Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1979 Springer-Verlag

About this chapter

Cite this chapter

Roggenkamp, K.W. (1979). Integral representations and presentations of finite groups. In: Integral Representations. Lecture Notes in Mathematics, vol 744. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0063060

Download citation

  • DOI: https://doi.org/10.1007/BFb0063060

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09546-0

  • Online ISBN: 978-3-540-35007-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics