Elementary abelian <Emphasis Type="Italic">p</Emphasis>-groups of rank 2<Emphasis Type="Italic">p</Emphasis>+3 are not CI-groups |
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Authors: | Gábor Somlai |
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Institution: | 1.Department of Algebra and Number Theory,E?tv?s University,Budapest,Hungary |
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Abstract: | For every prime p>2 we exhibit a Cayley graph on
\mathbbZp2p+3\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 of Muzychuk and Spiga concerning the problem. |
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