proposition: Lemma dprod_nil A B G : A \x B = G -> nilpotent G = nilpotent A && nilpotent B.
proof: Proof. by case/dprodP=> [[H K -> ->] <- cHK _]; rewrite mulg_nil. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(fintype div bigop prime finset fingroup morphism) mathcomp(automorphism quotient commutator gproduct) mathcomp(gfunctor center gseries cyclic)