29 research outputs found

    On the proportion of derangements and on suborbits in finite transitive groups

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    We find a lower bound on the proportion of derangements in a finite transitive group that depends on the minimal nontrivial subdegree. As a consequence, we prove that, if Γ\Gamma is a GG-vertex-transitive digraph of valency d≥1d\ge 1, then the proportion of derangements in GG is greater than 1/2d1/2d.Comment: 7 page
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