Local Analysis for the Odd Order Theorem. (= London Mathematical Society Lecture Note Series (LMS), Volume 188). Erstausgabe.

Bender, Helmut and George Glauberman; Carlip, Walter (assistance)

ISBN 10: 0521457165 / ISBN 13: 9780521457163

Published by Cambridge University Press, Cambridge, New York, Melbourne, 1994

About this Item

Kartonierte Broschur mit Rücken- und Deckeltitel. Der obere Rückenrand mit kleiner Bereibung, das Papier leicht nachgedunkelt, ansonsten guter bis sehr guter Erhaltungszustand. "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 interestfinite 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 foster further improvements." (Verlagstext) Helmut Bender (* 21. August 1942 in Wehrheim) ist ein deutscher Mathematiker, der sich mit Gruppentheorie (endliche Gruppen) befasst und Professor an der Christian-Albrechts-Universität zu Kiel war. Bender studierte ab 1962 Mathematik an der Johann-Wolfgang-Goethe-Universität Frankfurt am Main mit dem Diplom 1966 und der Promotion bei Reinhold Baer 1967 (Endlich zweifach transitive Permutationsgruppen, deren Involutionen keine Fixpunkte haben). 1967/68 war er Assistant Professor an der University of Illinois at Urbana-Champaign. Danach arbeitete er an der Johannes-Gutenberg-Universität Mainz, an der er sich 1969 habilitierte und danach Privatdozent und 1971 außerplanmäßiger Professor war. 1970/71 war er außerdem Associate Professor an der University of Illinois at Chicago. 1972 wurde er Professor in Kiel mit einer ordentlichen Professur ab 1978. Er ist bekannt für Vereinfachungen des Satzes von Feit und Thompson (Odd Order Theorem), des Satzes von John H. Walter über die Klassifikation einfacher Gruppen mit abelschen Sylow-2-Untergruppen und des Satzes von Daniel Gorenstein und John H. Walter über einfache Gruppen mit Diedergruppen als Sylow-2-Untergruppen von 1964 (von Bender 1981 veröffentlicht). George Isaac Glauberman (* 3. März 1941 in New York City) ist ein US-amerikanischer Mathematiker, der sich mit Gruppentheorie (endliche Gruppen) befasst und Professor an der University of Chicago ist. Glauberman studierte am Polytechnic Institute of Brooklyn mit dem Bachelor-Abschluss 1961, an der Harvard University mit dem Master-Abschluss 1962 und wurde 1965 an der University of Wisconsin bei Richard Hubert Bruck promoviert (Fixed Point Sub-Groups that Contain Centralizers of Involution). Danach war er zunächst Instructor an der University of Chicago, an der er 1970 eine volle Professur erhielt. 1978/79 war er als Guggenheim Fellow an der Universität Oxford, und 1967 bis 1969 war er Sloan Research Fellow. 2012 wurde er Fellow der American Mathematical Society. 1970 war er eingeladener Sprecher auf dem Internationalen Mathematikerkongress in Nizza (Local and global properties of finite groups). (Wikipedia) In englischer Sprache. XI, (I), 174, (6) pages. Groß 8° (153 x 228mm).

Seller Inventory # BN32884

Bibliographic Details

• Title: Local Analysis for the Odd Order Theorem. (= London Mathematical Society Lecture Note Series (LMS), Volume 188). Erstausgabe.
• Publisher: Cambridge University Press, Cambridge, New York, Melbourne
• Publication Date: 1994
• Language: English
• ISBN 10: 0521457165
• ISBN 13: 9780521457163
• Binding: Softcover
• Edition: First Printing.
• Condition: gut
• Weight: 272 grams

About this title

Synopsis

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.