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

Abstract

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.

arXiv comment11 pages