Almost elusive permutation groups. (English) Zbl 1523.20004
A finite permutation group having no derangements, that is no fixed-point-free elements, of prime order is said to be elusive. The study and construction of elusive groups was initiated by P. J. Cameron et al. [J. Lond. Math. Soc., II. Ser. 66, No. 2, 325–333 (2002; Zbl 1015.20001)] in 2002. Extending this notion, we say that a finite permutation group \(G\) is almost elusive if it contains a unique conjugacy class of derangements of prime order. In this paper, it is shown that every quasiprimitive almost elusive group is either almost simple or \(2\)-transitive of affine type. Moreover, the authors classify all the almost elusive groups that are almost simple and primitive with socle an alternating group, a sporadic group or a rank one group of Lie type.
Reviewer: John Bamberg (Crawley)
Citations:
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