Corollary 2

Suppose that X is unlaceable and that the group G operates freely in X. There exists a unique group homomorphism $p:\pi_1(Y, f(o))\rightarrow G$ whose kernel contains the image of $\pi_1(X, o)$ and such that $p(\mathsf{N}(g)) =g$ for every $g\in G$. Moreover, $\pi_1(X, o)\rightarrow \pi_1(Y, f(o))-\overset{p}{\rightarrow}G$ is an extension of G by $\pi_1(X, o)$.