Skip to main content

Blocks and centers of group algebras

  • Conference paper
  • First Online:
Lectures on Rings and Modules

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 246))

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. E. Artin, C. Nesbitt and R. M. Thrall, Rings with minimum condition. Ann Arbor, 1948.

    Google Scholar 

  2. H. Bass, Algebraic K-Theory. New York, Amsterdam, 1968.

    Google Scholar 

  3. R. Brauer and C. Nesbitt, On the modular characters of groups. Annals of Mathematics (2) 42 (1941), 556–590.

    Article  MathSciNet  MATH  Google Scholar 

  4. R. Brauer, Zur Darstellungstheorie der Gruppen endlicher Ordnung I. Math. Z. 63 (1956), 406–444.

    Article  MathSciNet  MATH  Google Scholar 

  5. R. Brauer, Zur Darstellungstheorie der Gruppen endlicher Ordnung II. Math. Z. 72 (1959), 25–46.

    Article  MathSciNet  Google Scholar 

  6. R. Brauer, On blocks and sections in finite groups I. Amer. J. Math. 89 (1967), 1115–1136.

    Article  MathSciNet  MATH  Google Scholar 

  7. R. Brauer, On the first main theorem on blocks of characters of finite groups. Illinois J. Math. 14 (1970), 183–187.

    MathSciNet  MATH  Google Scholar 

  8. E. Cline, Modular representation theory. Lecture Notes, California Institute of Technology, Pasadena, 1966.

    Google Scholar 

  9. C. W. Curtis and I. Reiner, Representation theory of finite groups and associative algebras. New York, London, 1962.

    Google Scholar 

  10. W. Feit, Modular representation theory. Lecture Notes Yale University, New Haven, 1970.

    Google Scholar 

  11. P. Fong, On the characters of p-solvable groups. Transact. Amer. Math. Soc. 98 (1961), 263–284.

    MathSciNet  MATH  Google Scholar 

  12. A. Geddes, A short proof of the existence of coefficient fields for complete, equicharacteristic local rings. J. London Math. Soc. 29 (1954), 334–341.

    Article  MathSciNet  MATH  Google Scholar 

  13. J. A. Green, Blocks of modular representations. Math. Z. 79 (1962), 100–115.

    Article  MathSciNet  MATH  Google Scholar 

  14. J. A. Green, Some remarks on defect groups. Math. Z. 107 (1968), 133–150.

    Article  MathSciNet  MATH  Google Scholar 

  15. J. A. Green and S. E. Stonehewer, The radicals of some group algebras. J. Algebra 13 (1969), 137–142.

    Article  MathSciNet  MATH  Google Scholar 

  16. J. A. Green, Axiomatic representation theory for finite groups. J. Pure and Applied Algebra 1 (1971), 41–77.

    Article  MathSciNet  MATH  Google Scholar 

  17. M. Hall, The theory of finite groups. New York, 1959.

    Google Scholar 

  18. W. Hamernik and G. Michler, On Brauer's main theorem on blocks with normal defect groups. J. Algebra (to appear).

    Google Scholar 

  19. B. Huppert, Endliche Gruppen I. Berlin, Heidelberg, New York, 1967.

    Google Scholar 

  20. B. Huppert, Modulare Darstellungstheorie. Vorlesungsausarbeitung, Mainz, 1968.

    Google Scholar 

  21. I. Kaplansky, Projective modules. Annals of Math. 68 (1958), 372–377.

    Article  MathSciNet  MATH  Google Scholar 

  22. Y. Kawada, On blocks of group algebras of finite groups. Science reports of the Tokyo Kyoiku Daigaku A 9 (1966), 87–110.

    MathSciNet  MATH  Google Scholar 

  23. J. Lambek, Lectures on rings and modules. Waltham (Mass.), Toronto, London, 1966.

    Google Scholar 

  24. G. Michler, Conjugacy classes and blocks of group algebras. Symposium on "Associative algebras", Rome, November 23–26, 1970.

    Google Scholar 

  25. G. Michler, The blocks of p-nilpotent groups over arbitrary fields.

    Google Scholar 

  26. M. Nagata, Local rings. New York, 1962.

    Google Scholar 

  27. M. Osima, Notes on blocks of group characters. Math. J. Okayama University 4 (1955), 175–188.

    MathSciNet  MATH  Google Scholar 

  28. M. Osima, On block idempotents of modular group rings. Nagoya Math. J. 28 (1966), 429–433.

    Article  MathSciNet  MATH  Google Scholar 

  29. D. S. Passman, Central idempotents in group rings. Proc. Amer. Math. Soc. 22 (1969), 555–556.

    MathSciNet  MATH  Google Scholar 

  30. D. S. Passman, Blocks and normal subgroups. J. Algebra 12 (1969), 569–575.

    Article  MathSciNet  MATH  Google Scholar 

  31. W. F. Reynolds, Blocks and normal subgroups of finite groups. Nagoya Math. J. 22 (1963), 15–32.

    Article  MathSciNet  MATH  Google Scholar 

  32. W. F. Reynolds, Block idempotents and normal p-subgroups. Nagoya Math. J. 28 (1966), 1–13.

    Article  MathSciNet  MATH  Google Scholar 

  33. W. F. Reynolds, Twisted group algebras over arbitrary fields. Illinois J. Math. 15 (1971), 91–103.

    MathSciNet  MATH  Google Scholar 

  34. W. F. Reynolds, Blocks and F-class algebras of finite groups. To appear.

    Google Scholar 

  35. W. F. Reynolds. Sections and ideals of centers of group algebras. To appear.

    Google Scholar 

  36. A. Rosenberg, Blocks and centers of group algebras. Math. Z. 76 (1961), 209–216.

    Article  MathSciNet  MATH  Google Scholar 

  37. H. Spiegel, Das Radikal der modularen Gruppenalgebra einer endlichen Gruppe. Diplomarbeit, Tübingen, 1970.

    Google Scholar 

  38. O. E. Villamayor, On the semi-simplicity of group algebras I. Proc. Amer. Math. Soc. 9 (1958), 621–627.

    Article  MathSciNet  MATH  Google Scholar 

  39. O. E. Villamayor, On the semi-simplicity of group algebras II. Proc. Amer. Math. Soc. 10 (1959), 27–31.

    MathSciNet  MATH  Google Scholar 

  40. D. A. R. Wallace, Note on the radical of a group algebra. Proc. Cambridge Phil. Soc. 54 (1958), 128–130.

    Article  MathSciNet  MATH  Google Scholar 

  41. D. A. R. Wallace, On the radical of a group algebra. Proc. Amer. Math. Soc. 12 (1961), 133–137.

    Article  MathSciNet  MATH  Google Scholar 

  42. D. A. R. Wallace, Group algebras with central radicals. Proc. Glasgow Math. Assoc. 5 (1962), 103–108.

    Article  MathSciNet  MATH  Google Scholar 

  43. D. A. R. Wallace, Lower bounds for the radical of the group algebra of a finite p-soluble group. Proc. Edinburgh Math. Soc. (2) 16 (1968), 127–134.

    Article  MathSciNet  MATH  Google Scholar 

  44. H. N. Ward, The analysis of representations induced from a normal subgroup. Michigan Math. J. 15 (1968), 417–428.

    Article  MathSciNet  MATH  Google Scholar 

  45. H. Zassenhaus, The theory of groups. Göttingen, 1956.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1972 Springer-Verlag

About this paper

Cite this paper

Michler, G.O. (1972). Blocks and centers of group algebras. In: Lectures on Rings and Modules. Lecture Notes in Mathematics, vol 246. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0059569

Download citation

  • DOI: https://doi.org/10.1007/BFb0059569

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05760-4

  • Online ISBN: 978-3-540-37181-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics