title: Trying to annihilate group schemes of rank 4

abstract:
We know that for commutative finite flat group schemes
applying the group law the rank times annihilates the group scheme,
as a kind of analogue for groups of finite order.
The lowest rank group schemes for which
we don't know in general if this is true, that is in the
non-commutative case, are the ones with rank 4.
We try to compute if it's true that group schemes of rank 4 are
annihilated by applying the group law 4 times.
Unfortunately we will see that although the
number 4 is quite 'small', the associated equations are not so small.