LMS: 188 Local Analysis Order Thm (London Mathematical Society Lecture Note Series, Series Number 188) - Softcover

Bender, Helmut

Softcover

ISBN 10: 0521457165 ISBN 13: 9780521457163

Publisher: Cambridge University Press, 2008

Synopsis

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

About this title

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.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2008
• Language: English
• ISBN 10: 0521457165
• ISBN 13: 9780521457163
• Binding: Paperback
• Number of pages: 188