Concatenation-contranormal APS

Definition
An APS of groups $$(G,\Phi)$$ is termed concatenation-contranormal if for any natural numbers $$m,n$$, the image of the map:

$$\Phi_{m,n}:G_m \times G_n \to G_{m+n}$$

is a contranormal subgroup of $$G_{m+n}$$, i.e. its normal closure is the whole group $$G_{m+n}$$.