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London Mathematical Society Lecture Note Series #188: Local Analysis for the Odd Order Theoremby Helmut Bender
Synopses & ReviewsPublisher Comments: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 tourdeforce 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 FeitThompson theorem. Simpler, more detailed proofs are provided for some intermediate theorems. Recent results are used to shorten other proofs.
Synopsis:This book presents a new version of the local analysis section of the Feit — Thompson theorem. It includes a recent (1991) significant improvement by Feit and Thompson and a short revision by T. Peterfalvi of the separate final section of the second half of the proof.
Synopsis:Local analysis is the study of the centralizers and normalizers of nonidentity psubgroups of a group, with Sylowâ€™s theorem as the first main tool. This book presents a new version of the local analysis section of the Feit — Thompson theorem. It includes a recent (1991) significant improvement by Feit and Thompson and a short revision by T. Peterfalvi of the separate final section of the second half of the proof.
Synopsis:The book presents a new version of the local analysis section of the FeitThompson theorem.
Description:Includes bibliographical references (p. 167168) and index.
Table of ContentsPart 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. pGroups of small rank; 5. Narrow pgroups; 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 pstability.
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