finite flat commutative group schemes arising from Abelian varieties How are the finite flat group schemes $\mathcal{A}[\ell^n]$ arising from an Abelian scheme $\mathcal{A}/S$ singled out among other finite flat commutative group schemes of exponent $\ell^n$?
 A: Is the abelian scheme you consider a fixed one?
If the base is of characteristic $p$, and $l = p$ then the Lie algebra of $A[l]$ is isomorphic to $Lie(A)$, so you get a dimension condition.
For example, $\alpha_p \oplus \alpha_p$ cannot be embedded in an elliptic curve.
There are also more general condition your group scheme $G$ should satisfy.
Assume that $S$ is the spectrum of an Artinian algebra and that
$G$ is $p$-torsion with a trivial bi-nilpotent part.
We have an exact sequence:
$$ 0 \to G^{mult} \to G \to G^{et} \to 0$$
then the orders of $G^{mult}$ and $G^{et}$ must be equal if $G$ is the $p$-torsion of an abelian scheme.
On the other hand, in section (15.4) of the book "Commutative group schemes" of F. Oort, there is the following result:
Every finite flat commutative group scheme is a subgroup scheme of some abelian variety $A$.
A: I'm reminded of two papers by Maja Volkov, an erstwhile student of Jean-Marc Fontaine.  They are 
MR2148801 (2006a:14027) 
Volkov, Maja 
A class of $p$-adic Galois representations arising from abelian varieties over $\Bbb Q_p$.
Math. Ann.  331  (2005),  no. 4, 889–923. 
MR1837096 (2002d:11067) 
Volkov, Maja 
Les représentations $l$-adiques associées aux courbes elliptiques sur ${\Bbb Q}_p$. 
J. Reine Angew. Math. 535 (2001), 65–101.
