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有限域上典型群的几何学(第二版)(英文版)
  • 书号:7030105958
    作者:万哲先
  • 外文书名:
  • 丛书名:
  • 装帧:
    开本:B5
  • 页数:460
    字数:500000
    语种:
  • 出版社:科学出版社
    出版时间:2006-03-30
  • 所属分类:O 数理科学和化学 O69 应用化学
  • 定价: ¥76.00元
    售价: ¥60.80元
  • 图书介质:
    电子书

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目录

  • Preface to the Second Edition
    Preface
    Chapter 1 Affine Geometry over Finite Fields
    1.1 Vector Spaces and Matrices over Finite Fields
    1.2 Affine Spaces and Affine Groups over Finite Fields
    1.3 Quadrics in AG(n,Fq)for q Odd
    1.4 Quadrics in AG(n,Fq)for q Even
    1.5 Comments
    1.6 Exercises
    Chapter 2 Projective Geometry over Finite Fields
    2.1 Projective Spaces and Projective Groups over Finite Fields
    2.2 Quadrics in PG(n,Fq)
    2.3 Quadrics in PG(2,Fq)
    2.4 Ovals in PG(2,Fq)
    2.5 Comments
    2.6 Exercises
    Chapter 3 Geometry of Symplectic Groups over Finite Fields
    3.1 Symplectic Groups and Symplectic Spaces over Finite Fields
    3.2 Anzahl Theorems in Symplectic Geometry over Finite Fields
    3.3 Singular Symplectic Geometry over Finite Fields
    3.4 Symplectic Polarities and Polar Spaces Arising from Then
    3.5 Comments
    3.6 Exercises
    Chapter 4 Geometry of Pseudo-symplectic Groups over Finite Fields of Characteristic 2
    4.1 Pseudo-symplectic Groups over Finite Fields of Characteristic 2
    4.2 Pseudo-symplectic Geometry over Finite Fields of Characteristic 2
    4.3 Singular Pseudo-symplectic Geometry over Finite Fields of Characteristic 2
    4.4 Pseudo-symplectic Geometry over Finite Fields of Characteristic 2 Again
    4.5 Pseudo-symplectic Polarities
    4.6 Comments
    4.7 Exercises
    Chapter 5 Geometry of Unitary Groups over Finite Fields
    5.1 Unitary Geometry over Finite Felds
    5.2 Anzahl Theorems in Unitary Geometry over Finite Fields
    5.3 Singular Unitary Geometry over Finite Fields
    5.4 Unitary Polarities and Polar Spaces Arising from Them
    5.5 Hermitian varieties in PG(N,Fq2)and AG(n,Fq2)
    5.6 Comments
    5.7 Exercises
    Chpater 6 Geometry of Orthogonal Groups over Finite Fields of Odd Characteristic
    6.1 Orthogonal Geometry over Finite Felds of Odd Characteristic
    6.2 Anzahl Theorems in Orthogonal Geometry over Finite Fields of Odd Characteristic
    6.3 Singular Orthogonal Geometry over Finite Fields of Odd Characteristic
    6.4 Orthogonal Polarities and Polar Spaces Arising from Them
    6.5 Comments
    6.7 Exercises
    Chapter 7 Geometry of Orthogonal Groups over Finite Fields of Characteristic 2
    7.1 Orthogonal Geometry over Finite Fields of Characteristic 2
    7.2 Anzahl Theorems in Orthogonal Geometry over Finite Fields of Characteristic 2
    7.3 Singular Orthogonal Geometry over Finite Fields of Characteristic 2
    7.4 Polar Spaces Arising from Orthogonal Geometry over Finite Fields of Characteristic 2
    7.5 Comments
    7.6 Exercises
    Appendix A Axiomatic Projective Geometry
    A.1 Incidence Structures
    A.2 Axioms of Projective Planes and the Principle of Duality
    A.3 Finite Projective Planes
    A.4 Collineations in Projective Planes
    A.5 Desargues Plause
    A.6 Projective Spaces
    Appendix B Polar Spaces and Generalized Quadrangles
    B.1 Polar Spaces
    B.2 Generalized Quadrangles
    Appendix C Critical Problems
    C.1 A Critical Problem in Finite Vector Spaces
    C.2 Critical Problems in Finite Unitary Spaces
    C.3 A Critical Problem in Finite Symplectic Spaces
    C.4 Comments
    Appendix D Moor-Penrose Generalized Inverses of Matrices over Finite Fields
    D.1 Definition and Properties
    D.2 Construction of Enumeration of M-P Invertible Matrices
    D.3 Generalization to Matrices over Fq2
    D.4 Comments
    Appendix E Representations of Forms by Forms in a Finite Field
    E.1 Representations of Bilinear Forms
    E.2 Representations of Alternate Forms
    E.3 Representations of Hermitian Forms
    E.4 Representations of Quadratic Forms(Odd Characteristic Case)
    E.5 Representations of Quadratic Forms(Even Characteristic Case)
    E.6 Representations of Symmetric Bilinear Forms over Finite Fields of Even Characteristic
    E.7 Comments
    E.8 Exercises
    Bibliography
    Notation
    Index
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