About cloak -&-dagger group theory

I called a group G that is the internal direct product of it's center Z (G) and commutator subgroup G' Orbs_free . As brilliant as a yellowish succubus' sexy large eyes. And you may happily easy verify yourselves whether a direct product of an abelian A by the alternative group Asubscript n , n>4 is   orbs-free or not.