Elementary Abelian p-groups of rank 2p+3 are not CI-groups

摘要

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 ofrank greater than or equal to $2p+3$ is not a CI-group. The proof is elementaryand uses only multivariate polynomials and basic tools of linear algebra.Moreover, we apply our technique to give a uniform explanation for the recentworks concerning the bound.