Section NormalComplement.
Variables K H G : {group gT}.
Hypothesis complH_K : H \in [complements to K in G].
End NormalComplement.
(* Semi-direct product *)
(* Central product *)

Lemma cprod_ntriv A B : A != 1 -> B != 1 ->
A \* B =
if [&& group_set A, group_set B & B \subset 'C(A)] then A * B else set0.