Finite groups and finite geometries
著者
書誌事項
Finite groups and finite geometries
（Cambridge tracts in mathematics, 78）
Cambridge University Press, 2010
- : pbk
- タイトル別名
-
Yugengun to yugenkika
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注記
Originally published in Japanese as Yugengun to yugenkika by Iwanami shoten, Tokyo, Japan 1976 and 1st published in English by the Cambridge University Press 1982 as finite groups and finite geometries.
Includes index
内容説明・目次
内容説明
The purpose of this 1982 book is to present an introduction to developments which had taken place in finite group theory related to finite geometries. This book is practically self-contained and readers are assumed to have only an elementary knowledge of linear algebra. Among other things, complete descriptions of the following theorems are given in this book; the nilpotency of Frobneius kernels, Galois and Burnside theorems on permutation groups of prime degree, the Omstrom-Wagner theorem on projective planes, and the O'Nan and Ito theorems on characterizations of projective special linear groups. Graduate students and professionals in pure mathematics will continue to find this account of value.
目次
- 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.
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