Finite groups and finite geometries /
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| 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: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/475606 |
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
