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Cambridge Tracts in Mathematics #78: Finite Groups and Finite Geometries

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Synopses & Reviews

Publisher Comments:

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.

Synopsis:

A 1982 introduction to developments which had taken place in finite group theory related to finite geometries.

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 π-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 SΩ and AΩ; 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.

Product Details

ISBN:
9780521183789
Author:
Tsuzuku, T.
Publisher:
Cambridge University Press
Author:
Okuyama, T.
Author:
Sevenster, A.
Location:
Cambridge
Subject:
Mathematics - Algebra
Subject:
Algebra - General
Edition Description:
Trade paper
Series:
Cambridge Tracts in Mathematics
Series Volume:
78
Publication Date:
20101231
Binding:
TRADE PAPER
Language:
English
Pages:
342
Dimensions:
8.5 x 5.51 x 0.75 in 0.97 lb

Related Subjects

Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry
Science and Mathematics » Mathematics » Group Theory

Cambridge Tracts in Mathematics #78: Finite Groups and Finite Geometries New Trade Paper
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Product details 342 pages Cambridge University Press - English 9780521183789 Reviews:
"Synopsis" by , A 1982 introduction to developments which had taken place in finite group theory related to finite geometries.
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