In **Braid Groups** of *Kassel, Turaev*, it mentions that $\mathcal{B}\_n$ is a residually finite group. The definition that they give as a **residually finite group** is a group $G$ such that for each $g\in G-\{e\_G\}$ ($e\_G$ the identity of $G$), there exists an homomorphism $f$ to a finite group $H$ such that $f(g)\neq e\_H$. My question is:

How can I obtain the group $H$ for a given element $g\in \mathcal{B}\_n$ and the homomorphism that fulfills this?

I hope you can help me. Nice Holidays.