THEORY OF FINITE SIMPLE GROUPS II by Gerhard Michler ( 9780521764919 )

Item Details

Title:

THEORY OF FINITE SIMPLE GROUPS II
COMMENTARY ON THE CLASSIFICATION PROBLEMS

By:

Gerhard Michler

Format:

Hardback

List price:

£169.00

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£147.88

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£21.12

ISBN 10:

0521764912

ISBN 13:

9780521764919

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Publisher:

CAMBRIDGE UNIVERSITY PRESS

Pub. date:

4 February, 2010

Series:

New Mathematical Monographs No. 14

Pages:

746

Description:

A coherent explanation of the existence of the 26 known sporadic simple groups.

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.

Illustrations:

140 tables

Publication:

Imprint:

Cambridge University Press

Returns:

Returnable

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