S. D. Freedman

collaborators

3 papers

math.GR2026

An infinite family of counterexamples to the Polycirculant Conjecture

Saul D. Freedman, Melissa Lee

We disprove the Polycirculant Conjecture, which states that every transitive 2-closed permutation group is non-elusive, i.e. contains a derangement of prime order. In fact, we prov…

math.GR2026

On the generalised Saxl graphs of permutation groups

Saul D. Freedman, Hong Yi Huang, Melissa Lee +1

A base for a finite permutation group $G \leq Sym (I^c ◯)$ is a subset of $I^c ◯$ with trivial pointwise stabiliser in $G$ , and the base size of $G$ is the smallest size of a base…

math.GR2024

The non-commuting, non-generating graph of a finite simple group

Saul D. Freedman

Let $G$ be a group such that $G / Z (G)$ is finite and simple. The non-commuting, non-generating graph $I^ (G)$ of $G$ has vertex set $G ∖ Z (G)$ , with edges corresponding to pa…