Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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THE CHARACTER TABLE OF THE GROUP $GL_2(Q)$WHEN EXTENDED BY A CERTAIN GROUP OF ORDER TWO

  • Darafsheh, M.R. (Department of Mathematics and Computer Science, Faculty of Science, Tehran university) ;
  • Larki, F.Nowroozi (Department of Mathematics, Al-Zahra University)
  • Published : 2000.09.01

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Abstract

Let G denote either of the groups $GL_2(q)$ or $SL_2(q)$. Then ${\theta}$:G -> G given by ${\theta}(A)$ = ${(A^t)}^{-l}$, where $A^t$ denotes the transpose of the matrix A, is an automorphism of G. Therefore we may form the group G.$<{\theta}>$ which is the split extension of the group G by the cyclic group $<{\theta}>$ of order 2. Our aim in this paper is to find the complex irreducible character table of G.$<{\theta}>$.

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References

  1. Springer Ergeb. Math. v.14 Generators and relations for Discrete Groups H. S. M. Coxeter;W. Moser
  2. Algebras, Groups and Geometries v.15 Some Conjugacy Classes in Groups associated with the General Linear Groups M. R. Darafsheh
  3. Korean J. Comput. and Appl. Math. v.6 no.2 Equivalence classes of matrices in GL₂(q) and SL₂(q) M. R. Darafsheh;F. Nowroozi Larki
  4. Group Representation Theory, Part A L. Dornhoff
  5. Publications Mathematicae v.34 Extensions of Cuspidal Characters of $GL_m$(q) W. Feit
  6. Contemporary Mathematics v.153 Extending steinberg characters W. Feit
  7. Proc. London. Math. Soc. v.47 no.3 Properties of the Characters of the Finite General Linear Group Related to Transpose-inverse involution R. Gow
  8. Trans. Amer. Math. Soc. v.83 The Characters of the Finite General linear Groups J. A. Green
  9. Character Theory of Finite Groups I. M. Isaacs
  10. Encyclopedia of Mathematics and its Applications v.20 Finite Fields R. Lidl;H. Niederreiter
  11. Canad. J. Math. v.3 The Representations of GL(3, q), GL(4, q), PGL(3, q), and PGL(4, q) R. Steinberg