Finite Groups and Finite Geometries

Table of Contents

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.

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• Copyright Information Page (75 KB)
• Index (172 KB)
• Table of Contents (85 KB)
• Front Matter (264 KB)
• Marketing Excerpt (476 KB)