Basic Structure of Maximal Irreducible Solvable Subgroups

In this chapter, we will begin to consider the classification of maximal irreducible solvable subgroups of the classical groups \(\operatorname {GL}_n(q)\) , \(\operatorname {GSp}_n(q)\) , and \(\operatorname {GO}_n^{\varepsilon }(q)\) , where q is a power of some prime p. We start with Sect. 2.1, where we will fix the basic notation used for the rest of the book, and provide some preliminary results. Then analogously to the case of symmetric groups, we will split the analysis of maximal irreducible solvable subgroups into two cases: the metrically imprimitive case, and the metrically primitive case.