Maximality of the Groups Constructed

In this chapter, we will complete the classification of maximal irreducible solvable subgroups of \(\varDelta (V, \kappa )\) and \(I(V, \kappa )\) . When \(\kappa \neq 0\) , we will more generally classify metrically completely reducible maximal solvable subgroups of \(\varDelta (V, \kappa )\) and \(I(V, \kappa )\) . Furthermore, in the case where q is even and \(\kappa \) is a quadratic form, we will also classify metrically completely reducible maximal solvable subgroups of \(\varOmega (V, \kappa )\) .