Abstract Root Subgroups and Simple Groups of Lie-Type
Franz G. Timmesfeld
Gebundenes Buch

Abstract Root Subgroups and Simple Groups of Lie-Type

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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 [F...