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15.95 (2002)

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(A. Mann, Ch. Praeger). Suppose that all fixed-point-free elements of a transitive permutation group $G$ have prime order $p$. If $G$ is a finite $p$-group, must $G$ have exponent $p$?

Contributor: E. I. Khukhro

Progress

This is true for $p = 2, 3$; it is also known that the exponent of $G$ is bounded in terms of $p$ (A. Hassani, M. Khayaty, E. I. Khukhro, C. E. Praeger, J. Algebra, 214, no. 1 (1999), 317–337).

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