Finite Groups and Finite Geometries

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.