Concatenation-contranormal APS

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

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}.