Theory of Finite Simple Groups. With DVD-ROM. (= Reihe: New Mathematical Monographs, Volume 8). Erstausgabe.

Michler, Gerhard O.

ISBN 10: 0521866251 / ISBN 13: 9780521866255

Published by Cambridge University Press, Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo, 2006

About this Item

Blauer Pappeinband mit goldgeprägtem Rücken- und Deckeltitel, DVD-Rom in montierter Hinterdeckelhülle und Schutzumschlag. Der Umschlag etwas berieben bzw. mit leichten Kratzern, der Schnitte leicht berieben, der Kopfschnitt auch dezent fleckig, die ersten Seiten randknickig (Seitenrand), einzelne Seiten mit winzigem Knickchen der oberen Ecke oder kleinem Randknick, ansonsten guter Erhaltungszustand. "This book provides the first representation theoretic and algorithmic approach to the theory of abstract finite simple groups. It presents self-contained proofs of classical and new group order formulas, and a new structure theorem for abstract finite simple groups. This, and the famous Brauer-Fowler theorem, provides the theoretical background for the author's algorithm which constructs all finite simple groups G having a 2-central involution z with a given centralizer CG(z)=H. The methods presented are designed for the construction of matrix representations, permutation representations and character tables of large finite groups. The author constructs all the simple satellites of the known simple groups that are not uniquely determined by a given centralizer H. Uniform existence and uniqueness proofs are given for the modern sporadic simple groups discovered by Janko, Higman and Sims, Harada, and Thompson. This latter result proves a long standing open problem in the theory. The experimental results (courtesy of M. Weller) for Chapter 12 are documented in the accompanying DVD." (Verlagstext) Gerhard O. Michler (* 5. Mai 1938 in Braunschweig) ist ein deutscher Mathematiker, der sich mit Darstellungstheorie und Gruppentheorie beschäftigt. Michler wurde 1965 an der Johann Wolfgang Goethe-Universität Frankfurt am Main bei Reinhold Baer promoviert (Radikale und Sockel). Er absolvierte ein Postdoktorat an der Cornell University in Ithaca, New York, USA. Während dieser Zeit wurde seine Tochter Ruth I. Michler geboren. Er habilitierte sich 1968 an der Eberhard Karls Universität Tübingen, wurde 1973 ordentlicher Professor in Gießen und war danach ab Ende der 1970er Jahre Professor an der Universität Duisburg-Essen. Zurzeit ist er Adjunct Professor an der Cornell University (2010). Michler organisierte Tagungen zur Darstellungstheorie am Mathematischen Forschungsinstitut Oberwolfach mit Bertram Huppert und Jonathan L. Alperin. Zu seinen Doktoranden zählen Christine Bessenrodt, Karin Erdmann und Jochen Ziegenbalg. (Wikipedia) In englischer Sprache. IX, (III), 662, (6) pages. Groß 8° (155 x 234mm). Seller Inventory # BN33118

Bibliographic Details

Title: Theory of Finite Simple Groups. With DVD-ROM...

Publisher: Cambridge University Press, Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo

Publication Date: 2006

Binding: Hardcover/gebunden

Condition: gut

Dust Jacket Condition: Dust Jacket Included

Edition: First Edition.

About this title

Synopsis:

This book provides the first representation theoretic and algorithmic approach to the theory of abstract finite simple groups. It presents self-contained proofs of classical and new group order formulas, and a new structure theorem for abstract finite simple groups. This, and the famous Brauer-Fowler theorem, provides the theoretical background for the author's algorithm which constructs all finite simple groups G having a 2-central involution z with a given centralizer CG(z)=H. The methods presented are designed for the construction of matrix representations, permutation representations and character tables of large finite groups. The author constructs all the simple satellites of the known simple groups that are not uniquely determined by a given centralizer H. Uniform existence and uniqueness proofs are given for the modern sporadic simple groups discovered by Janko, Higman and Sims, Harada, and Thompson. This latter result proves a long standing open problem in the theory. The experimental results (courtesy of M. Weller) for Chapter 12 are documented in the accompanying DVD.

Review:

'The approach described and advocated by Michler in this book is remarkable in that it offers a uniform method that can, in principle, be used to prove computationally the existence and uniqueness of almost all the sporadic simple groups.' Bulletin of the American Mathematical Society