Abstract: Let $F$ be a local field, and $n\ge2$ an integer. Associated to $G=PGL(n,F)$ there is a Bruhat Tits building, which is a homogeneous tree in the case $n=2$. This tree is (usually) the Cayley graph of a free group, which can be embedded in $G$. In this talk I discuss groups which play a role analogous to that of the free group in the case $n\ge3$. One way to describe this is as follows: $G$ acts transitively on the vertices of the building; we seek subgroups of $G$ which act simply transitively on these vertices. These groups have a presentation of a very special form. They are interesting for a number of reasons, including because they a) are very explicit co-compact lattice subgroups of $PGL(n,F)$; b) are new examples of automatic groups, c) have Kazhdan's property (T), d) sometimes define new, non-classical buildings; e) are generated by automata; f) have been used to construct "Ramanujan complexes"