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21.29 (2026)

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Let $G \leqslant \text{Sym}(\Omega)$ be a finite primitive permutation group with a regular suborbit (that is, $G$ has a trivial 2-point stabiliser). Then is it true that for all $\alpha, \beta \in \Omega$, there exists $\gamma \in \Omega$ such that the 2-point stabilisers $G_{\alpha, \gamma}$ and $G_{\beta, \gamma}$ are both trivial?

Contributor: T. C. Burness, M. Giudici

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