  Let $A$ be a finite abelian $p$ group of rank at least $2$. We show that
$E^0(BA)/I_{tr}$, the quotient of the Morava $E$-cohomology of $A$ by the ideal
generated by the image of the transfers along all proper subgroups, contains
$p$-torsion. The proof makes use of transchromatic character theory.
