PUB - Publikationen an der Universität Bielefeld

We investigate presentation problems for certain split extensions of discrete matrix groups. In the soluble front, we classify finitely presented Abels groups over arbitrary commutative rings R in terms of their ranks and the Borel subgroup of SL(2,R). In the classical set-up we prove that, under mild conditions, a parabolic subgroup of a classical group is relatively finitely presented with respect to its extended Levi factor. This yields, in particular, a partial classification of finitely presented S-arithmetic parabolic groups. Furthermore, we consider higher dimensional finiteness properties and establish an upper bound on the finiteness length of groups that admit certain representations with soluble image.