Successive extensions of minimal p-divisible groups

We study truncated Barsotti-Tate groups of level one (BT1) and their extensions to p-divisible groups. Firstly we show that any BT1 contains a certain minimal BT1 as a non-zero subgroup scheme. This proves that any BT1 is written as a successive extension of minimal BT1's. Secondly we prove that any successive extension of minimal BT1's which is a BT1 can be extended to a certain successive extension of minimal p-divisible groups. As an application, we determine the optimal upper bound of the last Newton slopes of p-divisible groups with a given isomorphism type of p-kernel.