S. D. Freedman

activity

20142026

most citedThe non-commuting, non-generating graph of a nilpotent group

9 citations · 29 across the 13 of their papers we have counts for

collaborators

14 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.GR2024

On the generalised Saxl graphs of permutation groups

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

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

math.GR2023★ 1 cited

Spreading primitive groups of diagonal type do not exist

John Bamberg, Saul D. Freedman, Michael Giudici

The synchronisation hierarchy of finite permutation groups consists of classes of groups lying between 2-transitive groups and primitive groups. This includes the class of spreadin…

math.GR2023

The relational complexity of linear groups acting on subspaces

Saul D. Freedman, Veronica Kelsey, Colva M. Roney-Dougal

The relational complexity of a subgroup $G$ of $Sym (Ω)$ is a measure of the way in which the orbits of $G$ on $Ω^{k}$ for various $k$ determine the original action of $G$ . V…

math.GR2022

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 $Ξ (G)$ of $G$ has vertex set $G ∖ Z (G)$ , with edges corresponding to pai…

math.GR2022★ 3 cited

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

Saul D. Freedman

Let $G$ be a (finite or infinite) group such that $G / Z (G)$ is not simple. The non-commuting, non-generating graph $Ξ (G)$ of $G$ has vertex set $G ∖ Z (G)$ , with vertices $x$ …

math.GR2022★ 4 cited

Finite groups satisfying the independence property

Saul D. Freedman, Andrea Lucchini, Daniele Nemmi +1

We say that a finite group $G$ satisfies the independence property if, for every pair of distinct elements $x$ and $y$ of $G$ , either ${x, y}$ is contained in a minimal generating…

math.GR2022

Total closure for permutation actions of finite nonabelian simple groups

Saul D. Freedman, Michael Giudici, Cheryl Praeger

For a positive integer $k$ , a group $G$ is said to be totally $k$ -closed if for each set $Ω$ upon which $G$ acts faithfully, $G$ is the largest subgroup of $Sym (Ω)$ that l…

math.CO2022★ 1 cited

Tournaments and Even Graphs are Equinumerous

Gordon F. Royle, Cheryl E. Praeger, S. P. Glasby +2

A graph is called odd if there is an orientation of its edges and an automorphism that reverses the sense of an odd number of its edges, and even otherwise. Pontus von Brömssen (né…

math.GR2020★ 9 cited

The intersection graph of a finite simple group has diameter at most 5

Saul D. Freedman

Let $G$ be a non-abelian finite simple group. In addition, let $Δ_{G}$ be the intersection graph of $G$ , whose vertices are the proper nontrivial subgroups of $G$ , with distinct subg…

math.GR2020★ 9 cited

The non-commuting, non-generating graph of a nilpotent group

Peter J. Cameron, Saul D. Freedman, Colva M. Roney-Dougal

For a nilpotent group $G$ , let $Ξ (G)$ be the difference between the complement of the generating graph of $G$ and the commuting graph of $G$ , with vertices corresponding to central…

math.GR2018★ 1 cited

On $p$ -groups with automorphism groups related to the exceptional Chevalley groups

Saul D. Freedman

Let $G^$ be the finite simply connected version of an exceptional Chevalley group, and let $V$ be a nontrivial irreducible module, of minimal dimension, for $G^$ over its f…

math.GR2017★ 1 cited

On $p$ -groups with automorphism groups related to the Chevalley group $G_{2} (p)$

John Bamberg, Saul D. Freedman, Luke Morgan

Let $p$ be an odd prime. We construct a $p$ -group $P$ of nilpotency class two, rank seven and exponent $p$ , such that $Aut (P)$ induces $N_{\mathrm{GL}(7,p)}(G_2(p)) = Z(\m…

quant-ph2014

Fault-Tolerant Quantum Walks

S. D. Freedman, Y. H. Tong, J. B. Wang

Quantum walks are expected to serve important modelling and algorithmic applications in many areas of science and mathematics. Although quantum walks have been successfully impleme…

An infinite family of counterexamples to the Polycirculant Conjecture

On the generalised Saxl graphs of permutation groups

Spreading primitive groups of diagonal type do not exist

The relational complexity of linear groups acting on subspaces

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

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

Finite groups satisfying the independence property

Total closure for permutation actions of finite nonabelian simple groups

Tournaments and Even Graphs are Equinumerous

The intersection graph of a finite simple group has diameter at most 5

The non-commuting, non-generating graph of a nilpotent group

On p-groups with automorphism groups related to the exceptional Chevalley groups

On p-groups with automorphism groups related to the Chevalley group G2​(p)

Fault-Tolerant Quantum Walks

On $p$ -groups with automorphism groups related to the exceptional Chevalley groups

On $p$ -groups with automorphism groups related to the Chevalley group $G_{2} (p)$