Henry Bradford

activity

20142026

most citedUniform Diameter Bounds in Branch Groups

1 citations · 3 across the 20 of their papers we have counts for

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23 papers · 1 filter

math.GR2026

Co-intersection graphs of nonabelian finite simple groups have diameter two

Henry Bradford, Kamilla Rekvényi

Let $G$ be a finite group. The co-intersection graph $Δ_{G}^{c}$ of $G$ has as its vertices the nontrivial proper subgroups of $G$ , with edges joining those pairs of subgroups which i…

math.GR2026

Mixed identities for simple locally finite groups

Henry Bradford, Kıvanç Ersoy, Jakob Schneider +1

A mixed identity of a group is a nontrivial word with constants that vanishes under every substitution of its variables. We derive lower bounds for the length of mixed identities i…

math.GR2026

Groups with arbitrarily poor permutation stability

Henry Bradford

We propose a quantitative notion of permutation stability for finitely generated groups. Our notion is related to, but distinct from, the ``stability rate'' introduced by Becker an…

math.GR2026

Sofic actions, halo products, and metric approximations of groups

Vadim Alekseev, Henry Bradford

We introduce the notion of a ``sofic $C$ -action'' of one group on another by automorphisms, for $C$ a class of groups. We show that if $C$ is the clas…

math.GR2025

Non-solutions to mixed equations in acylindrically hyperbolic groups coming from random walks

Henry Bradford, Alessandro Sisto

A mixed equation in a group $G$ is given by a non-trivial element $w (x)$ of the free product $G * Z$ , and a solution is some $g \in G$ such that $w (g)$ is the identity.…

math.GR2025

Groups of arbitrary lawlessness growth

Henry Bradford, Jacob Willis

For a finitely generated lawless group $Γ$ and $n \in N$ , let $A_{Γ} (n)$ be the minimal positive integer $M_{n}$ such that for all nontrivial reduced words $w$ of l…

math.GR2024

On the spectrum of residual finiteness growth functions

Henry Bradford

In [K. Bou-Rabee, B. Seward, J. Reine Angwe. Math. 2016] Bou-Rabee and Seward constructed examples of finitely generated residually finite groups $G$ whose residual finiteness grow…

math.GR2023

Non-singular word maps for linear groups

Henry Bradford, Jakob Schneider, Andreas Thom

We study the word image of words with constants in $GL (V)$ and show that it is large provided the word satisfies some natural conditions on its length and its critical consta…

math.GR2023

GAGTA 2023 Problem Session

Henry Bradford, Christopher H. Cashen, Francesco Fournier-Facio +2

The conference `Geometric and Asymptotic Group Theory with Applications (GAGTA) 2023: Groups and Dynamics' took place at the Erwin Schrödinger Institute on July 17-21. These are th…

math.GR2023

The length of mixed identities for finite groups

Henry Bradford, Jakob Schneider, Andreas Thom

We prove that there exists a constant $c > 0$ such that any finite group having no non-trivial mixed identity of length $\leq c$ is an almost simple group with a simple group of Lie…

math.GR2023

On the length of non-solutions to equations with constants in some linear groups

Henry Bradford, Jakob Schneider, Andreas Thom

We show that for any finite-rank free group $Γ$ , any word-equation in one variable of length $n$ with constants in $Γ$ fails to be satisfied by some element of $Γ$ of word-length $…

math.GR2022

Local permutation stability

Henry Bradford

We introduce a notion of "local stability in permutations" for finitely generated groups. If a group is sofic and locally stable in our sense, then it is also locally embeddable in…

math.GR2022

Hopfian wreath products and the stable finiteness conjecture

Henry Bradford, Francesco Fournier-Facio

We study the Hopf property for wreath products of finitely generated groups, focusing on the case of an abelian base group. Our main result establishes a strong connection between…

math.GR2022

Controlling LEF growth in some group extensions

Henry Bradford

We study the LEF growth function of a finitely generated LEF group $Γ$ , which measures the orders of finite groups admitting local embeddings of balls in a word metric on $Γ$ . We p…

math.GR2022★ 1 cited

Quantifying lawlessness in finitely generated groups

Henry Bradford

We introduce a quantitative notion of lawlessness for finitely generated groups, encoded by the "lawlessness growth function" $A_{Γ} : N \to N$ . W…

math.GR2021★ 1 cited

Topological full groups of minimal subshifts and quantifying local embeddings into finite groups

Henry Bradford, Daniele Dona

We investigate quantitative aspects of the LEF property for subgroups of the topological full group $[[σ]]$ of a two-sided minimal subshift over a finite alphabet, measured via th…

math.GR2021

Quantifying local embeddings into finite groups

Henry Bradford

We study a function $L_{Γ}$ which quantifies the LEF (local embeddability into finite groups) property for a finitely generated group $Γ$ . We compute this "LEF growth" func…

math.GR2018

Short Laws for Finite Groups of Lie Type

Henry Bradford, Andreas Thom

We produce new short laws in two variables valid in finite groups of Lie type. Our result improves upon results of Kozma and the second named author, and is sharp up to logarithmic…

math.GR2017

Constructing Directed Cayley Graphs of Small Diameter: A Potent Solovay-Kitaev Procedure

Henry Bradford

Let $Γ$ be a group and $(Γ_{n})_{n = 1}^{\infty}$ be a descending sequence of finite-index normal subgroups. We establish explicit upper bounds on the diameters of the directed Cayley…

math.GR2017★ 1 cited

Uniform Diameter Bounds in Branch Groups

Henry Bradford

Let $G$ be either the Grigorchuk $2$ -group or one of the Gupta-Sidki $p$ -groups. We give new upper bounds for the diameters of the quotients of $G$ by its level stabilisers, as wel…

math.GR2017

Short Laws for Finite Groups and Residual Finiteness Growth

Henry Bradford, Andreas Thom

We prove that for every $n \in N$ and $δ > 0$ there exists a word $w_{n} \in F_{2}$ of length $n^{2/3} lo g (n)^{3 + δ}$ which is a law for every finite group of order at most $n$ .…

math.GR2015

Expansion, Random Walks and Sieving in $S L_{2} (F_{p} [t])$

Henry Bradford

We construct new examples of expander Cayley graphs of finite groups, arising as congruence quotients of non-elementary subgroups of $S L_{2} (F_{p} [t])$ modulo certain square…

math.GR2014

New Uniform Diameter Bounds in Pro- $p$ Groups

Henry Bradford

We give new upper bounds for the diameters of finite groups which do not depend on a choice of generating set. Our method exploits the commutator structure of certain profinite gro…

Co-intersection graphs of nonabelian finite simple groups have diameter two

Mixed identities for simple locally finite groups

Groups with arbitrarily poor permutation stability

Sofic actions, halo products, and metric approximations of groups

Non-solutions to mixed equations in acylindrically hyperbolic groups coming from random walks

Groups of arbitrary lawlessness growth

On the spectrum of residual finiteness growth functions

Non-singular word maps for linear groups

GAGTA 2023 Problem Session

The length of mixed identities for finite groups

On the length of non-solutions to equations with constants in some linear groups

Local permutation stability

Hopfian wreath products and the stable finiteness conjecture

Controlling LEF growth in some group extensions

Quantifying lawlessness in finitely generated groups

Topological full groups of minimal subshifts and quantifying local embeddings into finite groups

Quantifying local embeddings into finite groups

Short Laws for Finite Groups of Lie Type

Constructing Directed Cayley Graphs of Small Diameter: A Potent Solovay-Kitaev Procedure

Uniform Diameter Bounds in Branch Groups

Short Laws for Finite Groups and Residual Finiteness Growth

Expansion, Random Walks and Sieving in SL2​(Fp​[t])

New Uniform Diameter Bounds in Pro-p Groups

Expansion, Random Walks and Sieving in $S L_{2} (F_{p} [t])$

New Uniform Diameter Bounds in Pro- $p$ Groups