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- W1567271607 abstract "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 pi-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 SOMEGA and AOMEGA 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." @default.
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- W1567271607 date "2010-01-01" @default.
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- W1567271607 title "Finite groups and finite geometries" @default.
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