  We consider the distribution of p-power group schemes among the torsion of
abelian varieties over finite fields of characteristic p, as follows. Fix
natural numbers g and n, and let $\xi$ be a non-supersingular principally
quasipolarized Barsotti-Tate group of level n. We classify the F_q-rational
forms $\xi^\alpha$ of $\xi$. Among all principally polarized abelian varieties
X/F_q of dimension g with p^n-torsion geometrically isomorphic to \xi, we
compute the frequency with which X[p^n] is isomorphic to $\xi^\alpha$. The
error in our estimate is bounded by $D/\sqrt{q}$ where D depends on g, n and p,
but not on $\xi$.
