Abstract Root Subgroups
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In this chapter we introduce the notion of a group generated by a class of abstract root subgroups together with certain specializations of it, namely k-root subgroups and abstract transvection groups. After discussing some examples, i. e. classical groups, we start to develop the elementary general theory of groups generated by a class of abstract root subgroups. Finally in §5 we show that each simple group of Lie type (in a general sense) is generated by a class of abstract root subgroups. The results of this chapter are, if not mentioned otherwise, from [Tim90a], [Tim91], [Tim99] or [Tim00b].
KeywordsConjugacy Class Parabolic Subgroup Polar Space Division Ring Singular Line
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