Involutive automorphisms of $N_{\circ }^{\circ }$ groups of finite Morley rank

We classify a large class of small groups of finite Morley rank: $N_{\circ }^{\circ }$-groups which are the infinite analogues of Thompson’s $N$-groups. More precisely, we constrain the $2$-structure of groups of finite Morley rank containing a definable, normal, non-soluble, $N_{\circ }^{\circ }$-subgroup.