Local analysis for the odd order theorem / Helmut Bender and George Glauberman, with the assistance of Walter Carlip.

Format:

Book

Author/Creator:

Bender, Helmut, 1942- author.

Glauberman, G., 1941- author.

Carlip, Walter, 1956- author.

Series:

London Mathematical Society lecture note series ; 188.

London Mathematical Society lecture note series ; 188

Language:

English

Subjects (All):

Feit-Thompson theorem.

Solvable groups.

Physical Description:

1 online resource (xi, 174 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 1994.

Language Note:

English

Summary:

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:

Ch. I. Preliminary Results. 1. 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

Ch. II. The Uniqueness Theorem. 7. The Transitivity Theorem. 8. The Fitting Subgroup of a Maximal Subgroup. 9. The Uniqueness Theorem

Ch. III. Maximal Subgroups. 10. The Subgroups M[subscript [alpha]] and A[subscript [sigma]]. 11. Exceptional Maximal Subgroups. 12. The Subgroup E. 13. Prime Action

Ch. IV. The Family of All Maximal Subgroups of G. 14. Maximal Subgroups of Type [actual symbol not reproducible] and Counting Arguments. 15. The Subgroup M[subscript F]. 16. The Main Results

App. A: Prerequisites and p-Stability

App. B: The Puig Subgroup

App. C: The Final Contradiction

App. D: CN-Groups of Odd Order

App. E: Further Results of Feit and Thompson.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 167-168) and index.

ISBN:

1-139-88653-3

1-107-36693-3

1-107-37158-9

1-107-36202-4

1-107-36849-9

1-299-40465-0

1-107-36447-7

0-511-89285-3

0-511-66559-8