In the proof of Theorem I(c) from this paper (pdf) (original zip), there is a proposition that says:
So by our choice of $g$ we get $\theta/p \mid \psi/p$ whence $\theta \mid \psi$.
(this is the 3rd complete sentence on the right-hand column of p. 204)
How do I use the "So by our choice of $g$ we get"? Why does $g$ not have any other degree? Why is the choice small as possible thus contravening c)?