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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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