Soluble Linear Groups
Direct computation shows that the triangular group Tr(n, F) is soluble of derived length at most (1- [-log2 n]) (see Exercise 1.3). By 2.3 every extension of a subgroup of Tr(n, F) by a finite soluble group is soluble and linear. The principal object of this chapter is to prove that every soluble linear group essentially has this form.
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