2 problems

Let $L$ be a flag complex, let $\varphi\colon A_L\to\mathbb{Z}$ be an epimorphism, and let $BB_L^\varphi$ be the associated Artin kernel. Suppose $BB_L^\varphi$ is of type…

Let $M$ be an aspherical closed manifold. Consider a descending chain of subgroups … such that each $G_i$ is normal in $G=\pi_1(M)$, the index $[G:G_i]$ is finite, and…