  A closed Riemann surface $S$ is called a generalized Fermat curve of type
$(p,n)$, where $n,p \geq 2$ are integers such that $(p-1)(n-1)>2$, if it admits
a group $H \cong {\mathbb Z}_{p}^{n}$ of conformal automorphisms with quotient
orbifold $S/H$ of genus zero with exactly $n+1$ cone points, each one of order
$p$; in this case $H$ is called a generalized Fermat group of type $(p,n)$. In
this case, it is known that $S$ is non-hyperelliptic and that $H$ is its unique
generalized Fermat group of type $(p,n)$. Also, explicit equations for them, as
a fiber product of classical Fermat curves of degree $p$, are known. For $p$ a
prime integer, we describe those subgroups $K$ of $H$ acting freely on $S$,
together with algebraic equations for $S/K$, and determine those $K$ such that
$S/K$ is hyperelliptic.
