Local Analysis for the Odd Order Theorem

The book presents a new version of the local analysis section of the Feit–Thompson theorem.

Helmut Bender (Author), George Glauberman (Author)

9780521457163, Cambridge University Press

Paperback, published 27 January 1995

188 pages
22.9 x 15.2 x 1.1 cm, 0.28 kg

'This book is written well … the authors have succeeded both in simplifying the proof of the Odd Order Theorem and in making it accessible to a wider audience.' Paul Flavell, Bulletin of the London Mathematical Society

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. The book will make the first half of this remarkable proof accessible to readers familiar with just the rudiments of group theory.

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.

Subject Areas: Groups & group theory [PBG]