Finite Groups and Finite Geometries

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.

Introduction:
Notation and preliminaries
Groups
Algebraic structures
Vector spaces
Geometric structures
Fundamental Properties of Finite Groups:
The Sylow theorems
Direct products and semi-direct products
Normal series
Finite Abelian groups
p-groups
Groups with operators
Group extensions and the theorem of Schur-Zassenhaus
Normal ¿-complements
Normal p-complements
Representation of finite groups
Frobenius groups
Fundamental Theory of Permutation Groups:
Permutations
Transitivity and intransitivity
Primitivity and imprimitivity
Multiple transitivity
Normal subgroups
Permutation groups of prime degree
Primitive permutation groups
Examples - Symmetric Groups and General Linear Groups:
Conjugacy classes and composition series of the symmetric and alternating group
Conditions for being a symmetric or alternating group
Subgroups and automorphism groups of S¿ and A¿
Generators and fundamental relations for Sn and An
The structure of general semi-linear groups
Properties of PSL(V) as a permutation group (dim V ≥ 3)
Symmetric groups and general linear groups of low order
Finite Projective Geometry:
Projective planes and affine planes
Higher-dimensional projective geometry
Characterization of projective geometries
Finite Groups and Finite Geometries:
Designs constructed from 2-transitive groups
Characterization of projective transformation
Epilogue
Index
Table of Contents provided by Publisher. All Rights Reserved.

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

FREE SHIPPING

Amazon no longer offers textbook rentals. We do!

Finite Groups and Finite Geometries

Summary

Table of Contents

Supplemental Materials