Local Analysis for the Odd Order Theorem [Paperback]

The book presents a new version of the local analysis section of the FeitThompson theorem.In 1963 Walter Feit and John G. Thompson published a proof of a 1911 conjecture by Burnside that every finite group of odd order is solvable, which was a tour-de-force of mathematics and inspired intense effort to classify finite simple groups. This book presents a revision and expansion of the first half of the proof.In 1963 Walter Feit and John G. Thompson published a proof of a 1911 conjecture by Burnside that every finite group of odd order is solvable, which was a tour-de-force of mathematics and inspired intense effort to classify finite simple groups. This book presents a revision and expansion of the first half of the proof.In 1963 Walter Feit and John G. Thompson published a proof of a 1911 conjecture by Burnside that every finite group of odd order is solvable. This proof, which ran for 255 pages, was a tour-de-force of mathematics and inspired intense effort to classify finite simple groups. This book presents a revision and expansion of the first half of the proof of the Feit-Thompson theorem. Simpler, more detailed proofs are provided for some intermediate theorems. Recent results are used to shorten other proofs.Part I. Preliminary Results: 1. Notation and elementary properties of solvable groups; 2. General results on representations; 3. Actions of Frobenius groups and related results; 4. p-Groups of small rank; 5. Narrow p-groups; 6. Additional results; Part II. The Uniqueness Theorem: 7. The transitivity theorem; 8. The fitting subgroup of a maximal subgroup; 9. The uniqueness theorem; Part III. Maximal Subgroups: 10. The subgroups Ma and Me; 11. Exceptional maximal subgroups; 12. The subgroup E; 13. Prime action; Part IV. The Family of All Maximal Subgroups of G: 14. Maximal subgroups of type p and counting arguments; 15. The subgroup Mf; 16. The main results; Appendix; Prerequisites and p-stability. This book reflects the modern improvements of the p-lol“%