Skip to main content
SpringerLink
Log in

The character table of the groupGL2(Q) when extended by a certain group of order two

  • Published:
Korean journal of computational & applied mathematics Aims and scope Submit manuscript

Abstract

LetG denote either of the groupsGL 2(q) or SL2(q). Then θ :G →G given by θ(A) = (A t)t, whereA t denotes the transpose of the matrixA, is an automorphism ofG. Therefore we may form the groupG.θ> which is the split extension of the groupG by the cyclic group θ of order 2. Our aim in this paper is to find the complex irreducible character table ofG. θ.

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

Similar content being viewed by others

References

  1. H.S.M Coxeter, W.Moser,Generators and relations for Discrete Groups, Springer Ergeb. Math. 14(1964).

  2. M.R. Darafsheh,Some Conjugacy Classes in Groups associated with the General Linear Groups, Algebras, Groups and Geometries, Vol.15, (1998), 183–199.

    MathSciNet  MATH  Google Scholar 

  3. M.R. Darafsheh, F. Nowroozi Larki,Equivalence classes of matrices in GL 2(q) and SL2{q), Korean J.Comput.and Appl.Math., Vol.6, No.2(1999), 331–344.

    Article  MATH  Google Scholar 

  4. L. Dornhoff,Group Representation Theory, Part A, Marcel Dekker, New York, 1971.

    MATH  Google Scholar 

  5. W. Feit,Extensions of Cuspidal Characters of GL m(q), Publications Mathematicae,34(1987), 273–297.

    Article  MATH  Google Scholar 

  6. W. Feit,Extending Steinberg characters, Contemporary Mathematics Vol.153, 1993, 1–9.

    Article  MathSciNet  MATH  Google Scholar 

  7. R. Gow,Properties of the Characters of the Finite General Linear Group Related to Transpose-inverse involution, Proc.London.Math.Soc. (3),47 (1983), 493–506.

    Article  MathSciNet  MATH  Google Scholar 

  8. J.A. Green,The Characters of the Finite General Linear Groups, Trans. Amer. Math. Soc.80 (1955) 402–447.

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  10. R.Lidl and H.Niederreiter,Finite Fields, Encyclopedia of Mathematics and its Applications, Vol.20, Addison-Wesley, 1983.

  11. R. Steinberg,The Representations of GL(3, q),GL(4, q), PGL(Z,q) and PGL(4,q), Canad. J. Math.,3 (1951), 225–235.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of mathematics, Al-Zahra university, Tehran, Iran

    M. R. Darafsheh

  2. Department of Mathematics and Computer Science, Faculty of Science, Tehran university, Tehran, Iran

    F. Nowroozi Larki

Authors
  1. M. R. Darafsheh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Nowroozi Larki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. R. Darafsheh.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Darafsheh, M.R., Larki, F.N. The character table of the groupGL2(Q) when extended by a certain group of order two. Korean J. Comput. & Appl. Math. 7, 643–654 (2000). https://doi.org/10.1007/BF03012274

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03012274

AMS Mathematics Subject Classification

Key words and phrases

Search

Navigation