  For every prime $p > 2$ we exhibit a Cayley graph of $\mathbb{Z}_p^{2p+3}$
which is not a CI-graph. This proves that an elementary Abelian $p$-group of
rank greater than or equal to $2p+3$ is not a CI-group. The proof is elementary
and uses only multivariate polynomials and basic tools of linear algebra.
Moreover, we apply our technique to give a uniform explanation for the recent
works concerning the bound.
