  Let $(R,\mathfrak{m}, k)$ be a strictly local normal $k$-domain of positive
characteristic and $P$ be a prime divisor on $X=\text{Spec } R$. We study the
Galois category of finite covers over $X$ that are at worst tamely ramified
over $P$ in the sense of Grothendieck--Murre. Assuming that $(X,P)$ is a purely
$F$-regular pair, our main result is that every Galois cover $f \: Y \to X$ in
that Galois category satisfies that $\bigl(f^{-1}(P)\bigr)_{\text{red}}$ is a
prime divisor. We shall explain why this should be thought as a (partial)
generalization of a classical theorem due to S.S.~Abhyankar regarding the
\'etale-local structure of tamely ramified covers between normal schemes with
respect to a divisor with normal crossings. Additionally, we investigate the
formal consequences this result has on the structure of the fundamental group
representing the Galois category. We also obtain a characteristic zero analog
by reduction to positive characteristics following Bhatt--Gabber--Olsson's
methods.
