Section Hall.
Implicit Type gT : finGroupType.

Lemma SchurZassenhaus_trans_actsol gT (G A B : {group gT}) :
solvable A -> A \subset 'N(G) -> B \subset A <*> G ->
coprime #|G| #|A| -> #|A| = #|B| ->
exists2 x, x \in G & B :=: A :^ x.