Bender H., Glauberman G. Local Analysis for the Odd Order Theorem

Cambridge: Cambridge University Press, 1995. — 187 p. — (London Mathematical Society Lecture Note Series 188). — ISBN-13 9780521457163.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.Preliminary Results
Elementary Properties of Solvable Groups
General Results on Representations
Actions of Probenius Groups and Related Results
p-Groups of Small Rank
Narrow p- Groups
Additional Results
The Uniqueness Theorem
The Transitivity Theorem
The Fitting Subgroup of a Maximal Subgroup
The Uniqueness Theorem
Maximal Subgroups
The Subgroups Ma and Ma
Exceptional Maximal Subgroups
The Subgroup E
Prime Action
The Family of All Maximal Subgroups of G
Maximal Subgroups of Type £? and Counting Arguments
The Subgroup MF
The Main ResultsAppendix A. Prerequisites and p-Stability
Appendix B. The Puig Subgroup
Appendix C. The Final Contradiction
Appendix D. CiV-Groups of Odd Order
Appendix E. Further Results of Feit and Thompson