fundamental group of the complement of a fiber-type arrangement is an iterated almost-direct product of free groups on a finite number of generators (those free groups are exactly the fundamental groups of the fibers $F_i$ from Definition \[fibertype\]).

2.  \[Splitsolv\] If ${{\mathcal A}}$ is split solvable of type $m=(m_1, \dots, m_r)$ (see Section \[sect:special\] for the definition), then $\pi_1(M_{{{\mathcal A}}})$ is isomorphic to the product of free groups ${\mathbb{F}}_{m_1} \times \dots \times {\mathbb{F}}_{m_r}$.

\[lefschetz\] Concerning the fundamental group, notice that line arrangements in ${\mathbb{C}}{\mathbb{P}}^2$ are the general case, via the Lefschetz hyperplane section theorem. See [@DP] for more results in this direction.

Although algorithms that give a presentation for $\pi_1(M_{{{\mathcal A}}})$ have been developed, it is well known that $\pi_1(M_{{{\mathcal A}}})$ is not a combinatorial invariant (Rybnikov, [@Ryb]). Conversely, one may ask: does $\pi_1$ determine the intersection lattice? This time the answer is affirmative, for line arrangements, as long as we deal with the naturally $1$-marked fundamental group of the complement. More generally, for an arbitrary projective arrangement ${{\mathcal A}}$, the lattice is recovered up to some level (at least $2$) from $\pi_1(M_{{{\mathcal A}}})$ endowed with the natural $1$-marking (see [@CDP Theorem 2.1]).

Let $G$ be a group. Define a 