Groups Acting Generically Multiply Transitively on Solvable Groups

In this work, we complete the classification of generically multiply transitive actions of groups on solvable groups in the finite Morley rank setting. We prove that if G is a group of finite Morley rank acting definably, faithfully and generically m-transitively on a connected solvable group V of finite Morley rank where rk(V) m, then rk(V)=m, V is a vector space of dimension m over an algebraically closed field F, G GLₘ(F), and the action is equivalent to the natural action of GLₘ(F) on Fᵐ. This generalises our previous work arXiv:2107.09997.