Finite flat group schemes over local Artin rings

Let R be a local Artin ring with maximal ideal m and residue class field of characteristic p > 0. We show that every finite flat group scheme over R i s annihilated by its rank, whenever m(p) = pm = 0. This implies that any fi nite flat group scheme over an Artin ring the square of whose maximal ideal is zero, is annihilated by its rank.