Concatenation-normality-large APS

This article defines a property that can be evaluated for an APS of groups

Definition

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

$\Phi _{m,n}:G_{m}\times G_{n}\to G_{m+n}$

is a normality-large subgroup of $G_{m+n}$: in other words, its intersection with any nontrivial normal subgroup is again nontrivial.