Solution
= Solution
For a <free action of a group>, every <stabilizer subgroup> is trivial. Hence every <ramification index of a holomorphic map> is one, and the projection is an unramified <covering map> of <degree of a holomorphic map> $|G|$. The <Riemann-Hurwitz formula> reduces to
$$
\boxed{2g-2=|G|(2h-2),\qquad g-1=|G|(h-1).}
$$
This is also the multiplicativity of <Euler characteristic under a finite covering>.