Canonical subgroups via Breuil-Kisin modules

Let p > 2 be a rational prime and K/ℚ_p be an extension of complete discrete valuation fields. Let G be a truncated Barsotti-Tate group of level n, height h and dimension d over O_K with 0 < d < h. In this paper, we show that if the Hodge height of G is less than 1/(p^n-2(p + 1)), then there exists a finite flat closed subgroup scheme of G of order p^nd over O_K with standard properties as the canonical subgroup.