Abstract Root Subgroups and Simple Groups of Lie-Type

Language: English

Published by Birkhäuser, Birkhäuser Jun 2012, 2012

3034875967 / 9783034875967

Series: Book 11 of 29 - Monographs in Mathematics

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This item is printed on demand - Print on Demand Titel. Neuware -It was already in 1964 [Fis66] when B. Fischer raised the question: Which finite groups can be generated by a conjugacy class D of involutions, the product of any two of which has order 1, 2 or 37 Such a class D he called a class of 3-tmnspositions of G. This question is quite natural, since the class of transpositions of a symmetric group possesses this property. Namely the order of the product (ij)(kl) is 1, 2 or 3 according as {i,j} n {k,l} consists of 2,0 or 1 element. In fact, if I{i,j} n {k,I}1 = 1 and j = k, then (ij)(kl) is the 3-cycle (ijl). After the preliminary papers [Fis66] and [Fis64] he succeeded in [Fis71J, [Fis69] to classify all finite 'nearly' simple groups generated by such a class of 3-transpositions, thereby discovering three new finite simple groups called M(22), M(23) and M(24). But even more important than his classification theorem was the fact that he originated a new method in the study of finite groups, which is called 'internal geometric analysis' by D. Gorenstein in his book: Finite Simple Groups, an Introduction to their Classification. In fact D. Gorenstein writes that this method can be regarded as second in importance for the classification of finite simple groups only to the local group-theoretic analysis created by J. Thompson.Springer Nature c/o IBS, Benzstrasse 21, 48619 Heek 408 pp. Englisch.

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Title
Abstract Root Subgroups and Simple Groups of Lie-Type
Author
Franz G. Timmesfeld
Publisher
Birkhäuser, Birkhäuser Jun 2012
Publication year
2012
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3034875967
ISBN 13
9783034875967
Item weight
701 grams
Dimensions
244x170x23 mm
Series
Book 11 of 29: Monographs in Mathematics

buchversandmimpf2000

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