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Derangements in primitive permutation groups, with an application to character theory. (English) Zbl 1335.20001
Let $$G$$ be a transitive permutation group on a finite set $$S$$ of size at least 2. An element $$x$$ of $$G$$ is called a derangement if it acts fixed point freely on $$S$$. In the paper under review the authors study the number of conjugacy classes of derangements in $$G$$. In particular they classify finite transitive permutation groups with a single conjugacy class of derangements. They also give stronger results on finite almost simple primitive permutation groups according to their conjugacy class number.

##### MSC:
 20B15 Primitive groups 20C15 Ordinary representations and characters 20E45 Conjugacy classes for groups 20D60 Arithmetic and combinatorial problems involving abstract finite groups
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