Finite Groups and Finite Geometries

T. Tsuzuku (Autor)

Buch | Softcover

342 Seiten

2011
Cambridge University Press (Verlag)
978-0-521-18378-9 (ISBN)

Artikel merken

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.

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.

Erscheint lt. Verlag	17.2.2011
Reihe/Serie	Cambridge Tracts in Mathematics
Übersetzer	A. Sevenster, T. Okuyama
Zusatzinfo	Worked examples or Exercises
Verlagsort	Cambridge
Sprache	englisch
Maße	140 x 216 mm
Gewicht	440 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-521-18378-2 / 0521183782
ISBN-13	978-0-521-18378-9 / 9780521183789
Zustand	Neuware