Abstract Root Subgroups and Simple Groups of Lie-Type

1. Front Matter

   Pages i-xiii

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2. Rank One Groups

   • Franz Georg Timmesfeld

   Pages 1-66

3. Abstract Root Subgroups

   • Franz Georg Timmesfeld

   Pages 67-149

4. Classification Theory

   • Franz Georg Timmesfeld

   Pages 151-256

5. Root involutions

   • Franz Georg Timmesfeld

   Pages 257-312

6. Applications

   • Franz Georg Timmesfeld

   Pages 313-371

7. Back Matter

   Pages 373-389

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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.

• DEX
• Finite
• Group theory
• Lie
• Microsoft Access
• Natural
• algebra
• boundary element method
• buildings and generalized polygons
• class
• finite group
• knowledge
• polygon
• proof
• theorem

"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

• Mathematisches Institut, Justus-Liebig-Universität Giessen, Giessen, Germany

  Franz Georg Timmesfeld

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