Monographs in Mathematics

Abstract Root Subgroups and Simple Groups of Lie-Type

Authors: Timmesfeld, Franz Georg

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About this book

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.

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"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."

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Table of contents (5 chapters)

Buy this book

eBook $139.00
price for USA (gross)
  • ISBN 978-3-0348-7594-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.00
price for USA
  • ISBN 978-3-7643-6532-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $179.00
price for USA
  • ISBN 978-3-0348-7596-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Abstract Root Subgroups and Simple Groups of Lie-Type
Authors
Series Title
Monographs in Mathematics
Series Volume
95
Copyright
2001
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Verlag
eBook ISBN
978-3-0348-7594-3
DOI
10.1007/978-3-0348-7594-3
Hardcover ISBN
978-3-7643-6532-5
Softcover ISBN
978-3-0348-7596-7
Series ISSN
1017-0480
Edition Number
1
Number of Pages
XIII, 389
Topics