Finite groups and finite geometries /

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Bibliographic Details
Author / Creator:Tsuzuku, Toshirō, 1929-
Uniform title:Yūgengun to yūgen kika. English
Imprint:Cambridge [Eng.] ; New York : Cambridge University Press, [1982]
Description:x, 328 p. : ill. ; 22 cm.
Language:English
Japanese
Series:Cambridge tracts in mathematics. 78
Subject:Finite groups
Finite geometries
Finite geometries.
Finite groups.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/475606
Hidden Bibliographic Details
ISBN:0521222427
Notes:Translation of Yūgengun to yūgen kika.
Includes index.
Table of Contents:
  • Part I. Introduction
  • 1. Notation and preliminaries
  • 2. Groups
  • 3. Algebraic structures
  • 4. Vector spaces
  • 5. Geometric structures
  • Part II. Fundamental Properties of Finite Groups
  • 1. The Sylow theorems
  • 2. Direct products and semi-direct products
  • 3. Normal series
  • 4. Finite Abelian groups
  • 5. p-groups
  • 6. Groups with operators
  • 7. Group extensions and the theorem of Schur-Zassenhaus
  • 8. Normal ¿-complements
  • 9. Normal p-complements
  • 10. Representation of finite groups
  • 11. Frobenius groups
  • Part III. Fundamental Theory of Permutation Groups
  • 1. Permutations
  • 2. Transitivity and intransitivity
  • 3. Primitivity and imprimitivity
  • 4. Multiple transitivity
  • 5. Normal subgroups
  • 6. Permutation groups of prime degree
  • 7. Primitive permutation groups
  • Part IV. Examples - Symmetric Groups and General Linear Groups
  • 1. Conjugacy classes and composition series of the symmetric and alternating group
  • 2. Conditions for being a symmetric or alternating group
  • 3. Subgroups and automorphism groups of S¿ and A¿
  • 4. Generators and fundamental relations for Sn and An
  • 5. The structure of general semi-linear groups
  • 6. Properties of PSL(V) as a permutation group (dim V ≥ 3)
  • 7. Symmetric groups and general linear groups of low order
  • Part V. Finite Projective Geometry
  • 1. Projective planes and affine planes
  • 2. Higher-dimensional; projective geometry
  • 3. Characterization of projective geometries
  • Part VI. Finite Groups and Finite Geometries
  • 1. Designs constructed from 2-transitive groups
  • 2. Characterization of projective transformation
  • Epilogue
  • Index