Skip to main content
Log in

On the construction of irreducible characters in p-blocks with normal metacyclic defect groups

  • Articles
  • Published:
Science China Mathematics Aims and scope Submit manuscript

An Erratum to this article was published on 23 August 2012

Abstract

The author carries out a detailed study of p-blocks with normal metacyclic defect groups provided that p is odd and the defect groups are splitting and nonabelian. In particular, the author constructs all the irreducible ordinary and modular characters in this type of blocks. As a by-product, k(B) and l(B) are obtained.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Dietz J. Stable Splittings of Classifying Spaces of Metacyclic p-Groups (p odd). J Pure Appl Algebra, 1993, 90: 115–136

    Article  MathSciNet  MATH  Google Scholar 

  2. Feit W. The Representation Theory of Finite Groups. North-Holland, 1982

  3. Gao S. On Brauer’s k(B)-problem for blocks with metacyclic defect groups of odd order. Arch Math, 2011, 96: 507–512

    Article  MATH  Google Scholar 

  4. Grove L C. Groups and Characters. New York: John Wiley&Sons Inc, 1997

    Book  MATH  Google Scholar 

  5. Holloway M, Koshitani S, Kunugi N. Blocks with nonabelian defect groups which have cyclic subgroups of index p. Arch Math, 2010, 94: 101–116

    Article  MathSciNet  MATH  Google Scholar 

  6. Isaacs I M. Character Theory of Finite Groups. New York: Academic Press, 1976

    MATH  Google Scholar 

  7. Nagao H, Tsushima Y. Representations of Finite Groups. New York: Academic Press, 1987

    Google Scholar 

  8. Navarro G. Characters and Blocks of Finite Groups. Cambridge: Cambridge University Press, 1998

    Book  MATH  Google Scholar 

  9. Olsson J B. On Subpairs and Modular Representation Theory. J Algebra, 1982, 76: 261–279

    Article  MathSciNet  MATH  Google Scholar 

  10. Puttaswamaiah B M, Dixon J D. Modular Representations of Finite Groups. New York: Academic Press Inc, 1977

    MATH  Google Scholar 

  11. Robinson D J S. A Course in the Theory of Groups. New York: Springer-Verlag, 1996

    Book  Google Scholar 

  12. Sasaki H. The mod p cohomology algebras of finite groups with metacyclic sylow p-subgroups. J Algebra, 1997, 192: 713–733

    Article  MathSciNet  MATH  Google Scholar 

  13. Sambale B. Cartan matrices and Brauer’s k(B)-conjecture. J Algebra, 2011, 331: 416–427

    Article  MathSciNet  MATH  Google Scholar 

  14. Sambale B. Cartan matrices and Brauer’s k(B)-conjecture II. Algebra J, 2011, 337: 345–362

    Article  MathSciNet  MATH  Google Scholar 

  15. Sambale B. Fusion systems on metacyclic 2-groups. Preprint

  16. Sambale B. 2-Blocks with minimal nonabelian defect groups. J Algebra, 2011, 337: 261–284

    Article  MathSciNet  MATH  Google Scholar 

  17. Yang S. On Olsson’s conjecture for blocks with metacyclic defect groups of odd order. Arch Math, 2011, 96: 401–408

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sheng Gao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gao, S. On the construction of irreducible characters in p-blocks with normal metacyclic defect groups. Sci. China Math. 55, 1179–1188 (2012). https://doi.org/10.1007/s11425-011-4328-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-011-4328-0

Keywords

MSC(2010)

Navigation