Theory of Finite Simple Groups Ii (Hardcover)

Gerhard Michler

ISBN 10: 0521764912 / ISBN 13: 9780521764919

Published by Cambridge University Press, Cambridge, 2010

About this Item

Hardcover. This is a coherent explanation for the existence of the 26 known sporadic simple groups originally arising from many unrelated contexts. The given proofs build on the close relations between general group theory, ordinary character theory, modular representation theory and algorithmic algebra described in the first volume. The author presents a new algorithm by which 25 sporadic simple groups can be constructed (the smallest Mathieu group M11 can be omitted for theoretical reasons), and demonstrates that it is not restricted to sporadic simple groups. He also describes the constructions of various groups and proves their uniqueness whenever possible. The computational existence proofs are documented in the accompanying DVD. The author also states several open problems related to the theorem asserting that there are exactly 26 groups, and R. Brauer's warning that there may be infinitely many. Some of these problems require new experiments with the author's algorithm. This is a coherent explanation for the existence of the 26 known sporadic simple groups originally arising from many unrelated contexts. The given proofs build on the intimate relations between general group theory, ordinary character theory, modular representation theory and algorithmic algebra described in the first volume. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9780521764919

Bibliographic Details

• Title: Theory of Finite Simple Groups Ii (Hardcover)
• Publisher: Cambridge University Press, Cambridge
• Publication Date: 2010
• Language: English
• ISBN 10: 0521764912
• ISBN 13: 9780521764919
• Binding: Hardcover
• Condition: new

About this title

Synopsis

This is a coherent explanation for the existence of the 26 known sporadic simple groups originally arising from many unrelated contexts. The given proofs build on the close relations between general group theory, ordinary character theory, modular representation theory and algorithmic algebra described in the first volume. The author presents a new algorithm by which 25 sporadic simple groups can be constructed (the smallest Mathieu group M11 can be omitted for theoretical reasons), and demonstrates that it is not restricted to sporadic simple groups. He also describes the constructions of various groups and proves their uniqueness whenever possible. The computational existence proofs are documented in the accompanying DVD. The author also states several open problems related to the theorem asserting that there are exactly 26 groups, and R. Brauer's warning that there may be infinitely many. Some of these problems require new experiments with the author's algorithm.

About the Author

Gerhard Michler is an Emeritus Professor of the Institute of Experimental Mathematics at the University of Duisburg-Essen and Adjunct Professor at Cornell University.