Finite Groups and Finite Geometries [Paperback]

A 1982 introduction to developments which had taken place in finite group theory related to 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.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.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 OmstromWagner 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.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 SchurZassenhaus; 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. Mull£>