Local Analysis for the Odd Order Theorem (London Mathematical Society Lecture Note Series)

Bender, Helmut/ Glauberman, George

Cambridge University Press（1995/01発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 188 p.
• 言語 ENG
• 商品コード 9780521457163
• DDC分類 515

基本説明

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Full Description

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.

Contents

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.