I couldn't find any historical information about Schur-Zassenhaus theorem in many books or even papers which mention this theorem.
I think, Schur proved that if $G$ is a finite group and if $N$ is normal abelian subgroup such that $|N|$ and $|G/N|$ are co-prime, then there is a subgroup (complement) $H$ such that $G=NH$ and $N\cap H=1$. Then Zassenhaus extended this theorem excluding assumption that $N$ is abelian. In the book "The Theory of Groups" by Zassenhaus, the extended theorem appears only with name of Schur.
The questions I would like to ask are historical, and I am posting here, since I couldn't find much about this theorem, anywhere.
Q.1. Give the name of the paper where Schur proved (t)his theorem first.
Q.2. Has Zassenhaus published the extended theorem before including in his book?
Zassenhaus gives the proof of the extended theorem in his book (p.162 in Dover Edition, and p.~132 in AMS Chelsea Edition). After the proof, he says,
"It has been conjectured that any two complements of $N$ are conjugate in $G$..."
Zassenhaus gives the proof of the conjuncture (in his book) in the following cases: i) $N$ is abelian; ii) $N$ is solvable; iii)$G/N$ is solvable.
Now, it is known that, the conjecture is true, in general. (See Groups and Representations- Alperin, Bell, p.84, and Exer. 2, p,104). My third question is
Q.3 Where the proof of this conjecture appears first? (I mean, who proved the conjecture?)