Name: LMS: 188 Local Analysis Order Thm Revised ed. Edition
Author: Helmut Bender (Author)
ISBN: 0521457165

LMS: 188 Local Analysis Order Thm Revised ed. Edition book cover

LMS: 188 Local Analysis Order Thm Revised ed. Edition

Author(s): Helmut Bender (Author)

Publisher: Cambridge University Press
Publication Date: 21 Aug. 2008
Edition: Revised ed.
Language: English
Print length: 188 pages
ISBN-10: 9780521457163
ISBN-13: 0521457165

Book 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.

Editorial Reviews

Review

‘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

Book Description

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

From the Back Cover

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.

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LMS: 188 Local Analysis Order Thm Revised Edition

LMS: 188 Local Analysis Order Thm Revised ed. Edition

Book Description

Editorial Reviews

Review

Book Description

From the Back Cover

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