Automorphism Orbits and Element Orders in Finite Groups : Almost-Solubility and the Monster.

Cover
Title page
Chapter 1. Introduction
1.1. Statement of our main results
1.2. Overview of the proofs of Theorems 1.1.2 and 1.1.3
1.3. Some related open questions
Chapter 2. Notation
Chapter 3. Proof of Theorem 1.1.3
3.1. Sporadic groups
3.2. Alternating groups
3.3. Groups of Lie type
Chapter 4. Proof of Theorem 1.1.2(1)
Chapter 5. Proof of Theorem 1.1.2(2)
5.1. Reduction to semisimple groups
5.2. Two lemmas for working with partitions
5.3. Some auxiliary results on finite simple groups
5.4. Gaining some control over socle cosets in finite semisimple groups
5.5. Another equivalent reformulation of Theorem 1.1.2(2)
5.6. A bit of elementary number theory
5.7. Some results concerning the classes \Hcal_{ ̂, ̂, ̂}
5.8. More restrictions on finite semisimple groups with bounded \q-value
5.9. Completing the proof of Theorem 1.1.2(2)
Bibliography
Back Cover.