Introduction / Part I: |
Notation and preliminaries / 1: |
Groups / 2: |
Algebraic structures / 3: |
Vector spaces / 4: |
Geometric structures / 5: |
Fundamental Properties of Finite Groups / Part II: |
The Sylow theorems |
Direct products and semi-direct products |
Normal series |
Finite Abelian groups |
p-groups |
Groups with operators / 6: |
Group extensions and the theorem of Schur-Zassenhaus / 7: |
Normal α-complements / 8: |
Normal p-complements / 9: |
Representation of finite groups / 10: |
Frobenius groups / 11: |
Fundamental Theory of Permutation Groups / Part III: |
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 / Part IV: |
Conjugacy classes and composition series of the symmetric and alternating group |
Conditions for being a symmetric or alternating group |
Subgroups and automorphism groups of SΩ and AΩ |
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 / Part V: |
Projective planes and affine planes |
Higher-dimensional; projective geometry |
Characterization of projective geometries |
Finite Groups and Finite Geometries / Part VI: |
Designs constructed from 2-transitive groups |
Characterization of projective transformation |
Epilogue |
Index |
Introduction / Part I: |
Notation and preliminaries / 1: |
Groups / 2: |
Algebraic structures / 3: |
Vector spaces / 4: |
Geometric structures / 5: |