Geodesic
Elementary Abelian $p$-groups of rank $2p+3$ are not CI-groups
Journal of Algebraic Combinatorics, Tome 34 (2011) no. 3, pp. 323-335.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: For every prime $p>2$ we exhibit a Cayley graph on $\mathbb Z _{ p} ^{2 p+3}$ mathbbZ_p^2p+3 which is not a CI-graph. This proves that an elementary abelian $p$-group of rank greater than or equal to $2 p+3$ 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.
Keywords: keywords Cayley graph, CI-group, elementary abelian $p$-group 
@article{JAC_2011__34_3_a8,
     author = {Somlai, G\'abor},
     title = {Elementary {Abelian} $p$-groups of rank $2p+3$ are not {CI-groups}},
     journal = {Journal of Algebraic Combinatorics},
     pages = {323--335},
     publisher = {mathdoc},
     volume = {34},
     number = {3},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2011__34_3_a8/}
}
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Somlai, Gábor. Elementary Abelian $p$-groups of rank $2p+3$ are not CI-groups. Journal of Algebraic Combinatorics, Tome 34 (2011) no. 3, pp. 323-335. http://geodesic.mathdoc.fr/item/JAC_2011__34_3_a8/