Remarks on Galois rational covers

In this note we improve the theorem on Galois rational covers $X\dashrightarrow V$ for primitive Fano varieties $V$, recently proven by the author, in the two directions: we extend to the maximum the class of Galois groups $G$, for which the proof works, and relax the conditions that must be satisfied by the variety $V$ -- the divisorial canonicity alone is sufficient.