The structure of the Levi subgroups and the corresponding semidirect product decompositions depend on the specific series of groups. But note that we always require relative integral homology of groups of type $A_*$. For special linear groups over fields and for unitary groups over division rings, these subgroups of type $A_*$ are general linear groups. Hence, as mentioned above, we can use strong results on the homological stability of general linear groups to obtain homological stability of these series of groups.

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Variations of this method using an appropriate type filtration can probably be used to prove homological stability results for different series of reductive groups. As mentioned above, this could be used to study groups of type $E_6$, $E_7$ or $E_8$, or to compare group homology of groups of different types. In particular, relations between algebraic K-theory and hermitian K-theory could also be studied by choosing a different type enumeration of a group of type $C_{n+1}$, forcing $G'$ to be of type $A_n$ instead of type $C_n$.

Lattices in two-dimensional affine buildings {#sec:lattices_results}
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A *uniform lattice* is a discrete and cocompact subgroup in a locally compact topological group. We describe a new geometric construction method producing buildings of 