The random walk on upper triangular matrices over ℤ/m ℤ

We study a natural random walk on the n × n uni-upper triangular matrices, with entries in ℤ/m ℤ , generated by steps which add or subtract a uniformly random row to the row above. We show that the mixing time of this random walk is O(m^2n log n+ n^2 m^o(1)) . This answers a question of Stong and of Arias-Castro, Diaconis, and Stanley.