Factorizations of Almost Simple Groups with a Solvable Factor, and Cayley Graphs of Solvable Groups.

Cover
Title page
Chapter 1. Introduction
1.1. Factorizations of almost simple groups
1.2. -Arc-transitive Cayley graphs
1.3. Discussions and some open problems
Chapter 2. Preliminaries
2.1. Notation
2.2. Results on finite simple groups
2.3. Elementary facts concerning factorizations
2.4. Maximal factorizations of almost simple groups
Chapter 3. The factorizations of linear and unitary groups of prime dimension
3.1. Singer cycles
3.2. Linear groups of prime dimension
3.3. Unitary groups of prime dimension
Chapter 4. Non-classical groups
4.1. The case that both factors are solvable
4.2. Exceptional groups of Lie type
4.3. Alternating group socles
4.4. Sporadic group socles
Chapter 5. Examples in classical groups
5.1. Examples in unitary groups
5.2. Examples in symplectic groups
5.3. Examples in orthogonal groups of odd dimension
5.4. Examples in orthogonal groups of plus type
Chapter 6. Reduction for classical groups
6.1. Inductive hypothesis
6.2. The case that has at least two non-solvable composition factors
Chapter 7. Proof of Theorem 1.1
7.1. Linear groups
7.2. Symplectic Groups
7.3. Unitary Groups
7.4. Orthogonal groups of odd dimension
7.5. Orthogonal groups of even dimension
7.6. Completion of the proof
Chapter 8. -Arc-transitive Cayley graphs of solvable groups
8.1. Preliminaries
8.2. A property of finite simple groups
8.3. Reduction to affine and almost simple groups
8.4. Proof of Theorem 1.3 and Corollary 1.5
Appendix A. Tables for nontrivial maximal factorizations of almost simple classical groups
Bibliography
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