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8.75 (1982)

Solved

(A known problem). Suppose $G$ is a finite primitive permutation group on $\Omega$, and $\alpha, \beta$ are distinct points of $\Omega$. Does there exist an element $g \in G$ such that $\alpha g = \beta$ and $g$ fixes no point of $\Omega$?

Contributor: J. G. Thompson

Progress

Not always (P. Müller, On transitive sets of derangements in primitive groups, Archiv der Mathematik, 126, 551–556 (2026)).

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