Corpus ID: 221090656

On the Burness-Giudici Conjecture

@article{Chen2020OnTB,
  title={On the Burness-Giudici Conjecture},
  author={Huye Chen and Shao-Fei Du},
  journal={arXiv: Combinatorics},
  year={2020}
}
Let $G$ be a permutation group on a set $\Omega$. A subset of $\Omega$ is a base for $G$ if its pointwise stabilizer in $G$ is trivial. By $b(G)$ we denote the size of the smallest base of $G$. Every permutation group with $b(G)=2$ contains some regular suborbits. It is conjectured by Burness-Giudici in [4] that every primitive permutation group $G$ with $b(G)=2$ has the property that if $\alpha^g\not\in \Gamma$ then $\Gamma \cap \Gamma^g\neq \emptyset$, where $\Gamma$ is the union of all… Expand

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