Metrically Primitive Maximal Irreducible Solvable Subgroups

For a metrically primitive maximal irreducible solvable \(G \leq \varDelta (V,\kappa )\) , we have previously described the possible structures for a maximal abelian normal subgroup \(F_0\) of isometries in G. In this chapter, we move on to the next step and identify a certain subgroup \(F_0 \leq A \trianglelefteq G\) such that \(A/F_0\) is abelian. We will then be able to complete the recursive description of the general structure of maximal irreducible solvable subgroups of \(\varDelta (V, \kappa )\) .