Melissa Lee

collaborators

Showing math.GRShow all

4 papers · 1 filter

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.GR2025

Prime simplicial complexes of finite groups

The prime simplicial complex $I^(G)$ of a finite group $G$ is composed of all sets of primes $S$ where $G$ has an element of order the product of primes in $S$ , with the subsets pa…

math.GR2025

The Saxl hypergraph of a permutation group

Melissa Lee, Anthony Pisani

Given a permutation group $G \leq Sym (I^c ◯)$ , a subset $B$ of $I^c ◯$ is said to be a base if its pointwise stabiliser in $G$ is trivial, and the base size $b (G)$ is the minimum…