The subgroup structure of the finite classical groups /

With the classification of the finite simple groups complete, much work has gone into the study of maximal subgroups of almost simple groups. In this volume the authors investigate the maximal subgroups of the finite classical groups and present research into these groups as well as proving many new...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Kleidman, Peter
Otros Autores: Liebeck, M. W. (Martin W.), 1954-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge ; New York : Cambridge University Press, 1990.
Colección:London Mathematical Society lecture note series ; 129.
Temas:
Group theory.
Finite groups.
Groupes finis.
Théorie des groupes.
MATHEMATICS > Group Theory.
Finite groups
Group theory
Groupes, théorie des.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Title
  • Copyright
  • Preface
  • Standard notation and terminology
  • Contents
  • Chapter 1 Motivation and Setting for the Results
  • 1.1 Introduction
  • 1.2 The classical groups
  • 1.3 The alternating, sporadic and exceptional groups
  • Chapter 2 Basic Properties of the Classical Groups
  • 2.1 Introduction
  • 2.2 The linear groups
  • 2.3 The unitary groups
  • 2.4 The symplectic groups
  • 2.5 The orthogonal groups
  • 2.6 Orthogonal groups in odd dimension
  • 2.7 Orthogonal groups with Witt defect 0.
  • 2.8 Orthogonal groups with Witt defect 1
  • 2.9 Structure and isomorphisms
  • 2.10 Classical groups acting on their associated geometries
  • Chapter 3 The Statement of the Main Theorem
  • 3.1 Introduction
  • 3.2 How to determine the conjugacy amongst members of C
  • 3.3 How to determine the structure of members of C
  • 3.4 How to determine the overgroups of members of C
  • 3.5 The tables
  • Chapter 4 The Structure and Conjugacy of the Members of C
  • 4.0 Introduction
  • 4.1 The reducible subgroups C1
  • 4.2 The imprimitive subgroups C2.
  • 4.3 The field extension subgroups C3
  • 4.4 The tensor product subgroups C4
  • 4.5 The subfield subgroups C5
  • 4.6 The symplectic-type subgroups C6
  • 4.7 The tensor product subgroups C7
  • 4.8 The classical subgroups C8
  • Chapter 5 Properties of the Finite Simple Groups
  • 5.1 Basic properties of the simple groups
  • 5.2 Subgroups of the simple groups
  • 5.3 Representations of the simple groups
  • 5.4 Groups of Lie type: representations in the natural characteristic
  • 5.5 Further results on representations
  • Chapter 6 Non-maximal Subgroups in C: the Examples.

Ejemplares similares