Geodesic
Elementary abelian $p$-groups of rank greater than or equal to $4p-2$ are not CI-groups.
Journal of Algebraic Combinatorics, Tome 26 (2007) no. 3, pp. 343-355.

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

Summary: In this paper we prove that an elementary Abelian $p$-group of rank $4 p - 2$ is not a CI $^{(2)}$-group, i.e. there exists a 2-closed transitive permutation group containing two non-conjugate regular elementary Abelian $p$-subgroups of rank $4 p - 2$, see Hirasaka and Muzychuk (J. Comb. Theory Ser. A $94(2)$, 339-362, 2001). It was shown in Hirasaka and Muzychuk (loc cit) and Muzychuk (Discrete Math. 264(1-3), 167-185, 2003) that this is related to the problem of determining whether an elementary Abelian $p$-group of rank $n$ is a CI-group. As a strengthening of this result we prove that an elementary Abelian $p$-group $E$ of rank greater or equal to $4 p - 2$ is not a CI-group, i.e. there exist two isomorphic Cayley digraphs over $E$ whose corresponding connection sets are not conjugate in Aut $E$.
Keywords: keywords Cayley graph, CI-group, Schur ring, 2-closure 
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     author = {Spiga, Pablo},
     title = {Elementary abelian $p$-groups of rank greater than or equal to $4p-2$ are not {CI-groups.}},
     journal = {Journal of Algebraic Combinatorics},
     pages = {343--355},
     publisher = {mathdoc},
     volume = {26},
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     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2007__26_3_a3/}
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Spiga, Pablo. Elementary abelian $p$-groups of rank greater than or equal to $4p-2$ are not CI-groups.. Journal of Algebraic Combinatorics, Tome 26 (2007) no. 3, pp. 343-355. http://geodesic.mathdoc.fr/item/JAC_2007__26_3_a3/