Abstract Root Subgroups and Simple Groups of Lie-Type

Timmesfeld, Franz Georg

ISBN 10: 3764365323 / ISBN 13: 9783764365325

Published by Williston, Vermont, U.S.A.: Birkhauser, 2001

About this Item

Hardback in near fine condition with near fine condition dust jacket. Seller Inventory # 152049

Bibliographic Details

Title: Abstract Root Subgroups and Simple Groups of...

Publisher: Williston, Vermont, U.S.A.: Birkhauser

Publication Date: 2001

Binding: Hardcover

Condition: Near Fine

Dust Jacket Condition: Near Fine

About this title

Synopsis:

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.

Review:

"The book is well written: the style is concise but not hard and most of the book is not too difficult to read for a graduate student. Some parts of it are certainly suited for a class."

--Mathematical Reviews