If $R = F_q[t]$ is the polynomial ring over a finite field
then the group $SL_2(R)$ is not finitely generated. The group $SL_3(R)$ is
finitely generated but not finitely presented, while $SL_4(R)$ is
finitely presented. These examples are facets of a larger picture that
I will talk about.
- Algebra Seminar