Author

A. Rizzoli

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Preprint Sep 2026

Common neighbour conjectures for Saxl graphs fail at every base size

For a finite permutation group, a base is a set of points with trivial pointwise stabiliser, and the generalised Saxl graph records which pairs of points lie together in a base of minimum size. Burness and Giudici conjectured that any two vertices of the Saxl graph of a primitive group of base size two have a common ne...

A. Rizzoli, Adam R. Thomas · 1 citation

Preprint Sep 2026

Sylow synchronization in finite groups: the good case

Let $G$ be a finite solvable group such that, for any prime $p$ and any quotient $Q$ of $G$, there are two Sylow $p$-subgroups of $Q$ intersecting in $O_p(Q)$. Then, for every family $(P_i)_{i=1}^n$ of Sylow subgroups of $G$ for distinct primes $p_1,\ldots,p_n$, there exists $x \in G$ such that $P_i \cap P_i^x = O_{p_i...

Hong-Yi Huang, Francesca Lisi, A. Rizzoli et al. · 0 citations