Journal of applied mathematics & informatics

  • 제6권2호
  • /
  • Pages.433-446
  • /
  • 1999
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  • 2734-1194(pISSN)
  • /
  • 2234-8417(eISSN)
한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지

EQUIVALENCE CLASSES OF MATRICES IN $GL_2(Q)$ AND $SL_2(Q)$

  • Darafsheh, M.R. (Department of mathematics and computer science Tehran University and institue for studies in theoretical physics and mathematics Tehran) ;
  • Larki, F. Nowroozi (Department of mathematics and computer science Tehran University and Institute for studies in theoretical physics and mathematics)
  • 발행 : 1999.06.01

⟨ 이전 논문 다음 논문 ⟩

초록

Let G denote either of the groups $GL_2(q)$ or $SL_2(q)$. The mapping $theta$ sending a matrix to its transpose-inverse is an auto-mophism of G and therefore we can form the group $G^+$ = G.<$theta$>. In this paper conjugacy classes of elements in $G^+$ -G are found. These classes are closely related to the congruence classes of invert-ible matrices in G.

키워드

참고문헌

  1. Discrete Mathematics v.118 Congruence Classes of Matrices in GL₂(q) P.S.Bremser
  2. Groups and Geometry v.15 Some Conjugacy Classes in Groups associated with the General Linear Groups M.R.Darafsheh
  3. Group Representation Theory Part A L.Dornhoff
  4. Publicationes Mathematics v.34 Extensions of Cuspidal Characters of GLm(q) W.Fiet
  5. Linear Algebra and its Applications v.41 The Number of Equivalence Classes of Non-degenerate Bilinear and Sesquilnear Forms over a Finite Field R.Gow
  6. 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
  7. Encyclopedia of Mathematics and its Applicatons v.20 Finite Fields R.Lidl;H.Niederreiter
  8. Canad. J. Math. v.3 The Representations of GL(3,q), GL(4,q), PGL(3,q) and PGL(4,q) R.Steinberg
  9. J. Austral. Math. Soc. v.3 On the Conjugacy Classes in the Unitary, Symplectic and Orthogonal Groups G.E.Wall
  10. Finite Fields and their Application v.1 The Number of Congruence Classes in Mn(Fq) W.C.Waterhouse