Local analysis for the odd order theorem /

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Bibliographic Details
Author / Creator:	Bender, Helmut, 1942-
Imprint:	Cambridge [England] ; New York : Cambridge University Press, 1994.
Description:	1 online resource (xi, 174 pages) : illustrations.
Language:	English
Series:	London Mathematical Society lecture note series ; 188 London Mathematical Society lecture note series ; 188.
Subject:	Feit-Thompson theorem. Solvable groups. Feit-Thompson theorem. Solvable groups. Electronic books.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11181097

Hidden Bibliographic Details
Other authors / contributors:	Glauberman, G., 1941- Carlip, Walter, 1956-
ISBN:	9781107362024 1107362024 0521457165 9780521457163 1139886533 9781139886536 1107366933 9781107366930 1107371589 9781107371583 1107368499 9781107368491 1299404650 9781299404656 1107364477 9781107364479 0511892853 9780511892851 0511665598 9780511665592
Notes:	Includes bibliographical references (pages 167-168) and index. English. Print version record.
Summary:	In 1963 Walter Feit and John G. Thompson proved the Odd Order Theorem, which states that every finite group of odd order is solvable. The influence of both the theorem and its proof on the further development of finite group theory can hardly be overestimated. The proof consists of a set of preliminary results followed by three parts: local analysis, characters, and generators and relations (Chapters IV, V, and VI of the paper). Local analysis is the study of the centralizers and normalizers of non-identity p-subgroups, with Sylow's Theorem as the first main tool. The main purpose of the book is to present a new version of the local analysis of the Feit-Thompson Theorem (Chapter IV of the original paper and its preliminaries). 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. The book should interest finite group theorists as well as other mathematicians who wish to get a glimpse of one of the most famous and most forbidding theorems in mathematics. Current research may eventually lead to a revised proof of the entire theorem, but this goal is several years away. For the present, the authors are publishing this work as a set of lecture notes to contribute to the general understanding of the theorem and to further improvements.
Other form:	Print version: Bender, Helmut, 1942- Local analysis for the odd order theorem. Cambridge [England] ; New York : Cambridge University Press, 1994 0521457165

Table of 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.

Local analysis for the odd order theorem /

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