# Element structure of unitriangular matrix group of degree three over a finite discrete valuation ring

We assume that the residue field has size $q$ and characteristic $p$, with $r = \log_pq$. We denote by $l$ the length of the discrete valuation ring. The size of the ring is thus $q^l = p^{rl}$ and the order of the field is $q^{3l} = p^{3rl}$.