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21.27 (2026)

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(M. Larsen, A. Shalev, P. H. Tiep). A permutation on a set $\Omega$ is called a derangement if it has no fixed points in $\Omega$. Let $G$ be a finite simple transitive permutation group. Is it true that every element in $G$ is the product of two derangements?

Contributor: T. C. Burness

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