I am reading de la Harpe's book "Topics in Geometric Group Theory". On page 145, there is a theorem: Let $V$ be a complete $n$-Riemannian manifold with sectional curvature satisfying $K\ge 0$. Then there exist a finite normal subgroup $F_1$ of the fundamental group $\pi_1(V)$ and a short exact sequence of the form: $$ 1 \to \mathbb Z^k \to \pi_1(V)/F_1 \to F_2 \to 1 $$ where $k\le n$ and where $F_2$ is a finite group.
I have two questions:
1) why the author put $F_1$ in such a special position, why not absorb $F_1$ into $F_2$, since they are basically all finite group.
2) In other papers/books, peopole called a discrete, torsion free and cocompact subgroup of $O(n)\ltimes \mathbb R^n $ A Bieberbach group. So why "torsion free" is important?