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

2009/11/16 by Gábor Somlai, Somlai, Gabor
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Rings, Modules, and Algebras #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.0911.2991

openalex publication_date 2009/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For every prime p > 2 we exhibit a Cayley graph of 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.

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