Canonical subgroups of Barsotti-Tate groups

Let $S$ be the spectrum of a complete discrete valuation ring with fraction field of characteristic 0 and perfect residue field of characteristic $p\geq 3$\mathrm{.}Let$G$beatruncatedBarsotti-Tategroupoflevel1over$S$\mathrm{.}If\mathrm{‘}\mathrm{‘}$G$ is not too supersingular’', a condition that will be explicitly expressed in terms of the valuation of a certain determinant, we prove that we can canonically lift the kernel of the Frobenius endomorphism of its special fibre to a subgroup scheme of $G$, finite and flat over $S$. We call it the canonical subgroup of $G$.