sentences:  If "H" is normal in "G", then the mappings α and β are given by, respectively, α("k","h") = "k h k"− 1 and β("k", "h") = "k".In this case, "G" is an internal semidirect product of "H" and "K".If, in addition, "K" is normal in "G", then α("k","h") = "h".