Abstract
In this work, we construct fundamental domains for congruence subgroups of SL2(F-q[t]) and PGL(2)(F-q[t]). Our method uses Gekeler's description of the fundamental domains on the Bruhat-Tits tree X = Xq+1 in terms of cosets of subgroups. We compute the fundamental domains for a number of congruence subgroups explicitly as graphs of groups using the computer algebra system Magma. (C) 2010 Elsevier Inc. All rights reserved.