  For K a local field, it is shown that SL3(K) acts on a simply connected two
dimensional simplicial complex in which a single face serves as a fundamental
domain. From this it follows that SL3(K) is the generalized amalgamated product
of three subgroups. Specifically if K is the field of fractions of the discrete
valuation ring O, then SL3(K) is the amalgamation of three subgroups isomorphic
to SL3(O) along pairwise intersections. This generalizes a theorem of Ihara,
which gives the structure of SL2(K) as the amalgamated product of two groups in
analogous fashion.
