sentences:  To motivate this, let "G" = "HK" be an internal Zappa–Szép product of subgroups "H" and "K" of the group "G".For each "k" in "K" and each "h" in "H", there exist α("k","h") in "H" and β("k","h") in "K" such that "kh" = α("k","h") β("k","h").This defines mappings α