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

Somlai, Gábor (2011) Elementary abelian p-groups of rank 2p+3 are not CI-groups. JOURNAL OF ALGEBRAIC COMBINATORICS, 34 (3). pp. 323-335. ISSN 0925-9899 (print); 1572-9192 (online)

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Abstract

For every prime p>2 we exhibit a Cayley graph on 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 of Muzychuk and Spiga concerning the problem.

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