Requirement for Hall-$\pi$-subgroups to be conjugate (Wielandt) I am reading through Isaacs Theory of finite groups and towards the end of chapter 3 on "split extensions" there is mention of a theorem of Wielandt which states that if a finite group $G$ contains a nilpotent Hall-$\pi$-subgroup then all the Hall-$\pi$-subgroups of $G$ are conjugate. However I cannot find an exact statement and proof of this theorem in any text regarding the matter. Does anyone know of any such texts which could be of use? 

You can look at the Theorem and proof in Derek J.S. Robinson's "A course in the Theory of Groups" Chapter 9 (p. 258-259). It says: Let the finite group $G$ possess a nilpotent Hall $\pi$-subgroup $H$. Then every $\pi$-subgroup of $G$ is contained in a conjugate of $H$. In particular all Hall $\pi$-subgroups of $G$ are conjugate. (The proof is easy using a lemma of O.J. Schmidt, and I do not know any other that does not uses it). I hope I have helped you.
