Related papers: An Irrational-slope Thompson's Group

To each supersimple $2-(n,4,\lambda)$ design $\mathcal{D}$ one associates a `Conway groupoid,' which may be thought of as a natural generalisation of Conway's Mathieu groupoid associated to $M_{13}$ which is constructed from $\mathbb{P}_3$.…

We extend the concept of two-way forest diagrams, introduced by Belk and Brown in 2003, to represent elements of $F(n)$ as a pair of infinite, bounded $n$-ary forests together with an order-preserving bijection of the leaves. This…

Let $(G_n)_{n \in \mathbb{N}}$ be a sequence of groups equipped with a $d$-ary cloning system and denote by $\mathscr{T}_d(G_*)$ the resulting Thompson-like group. In previous work joint with Zaremsky, we obtained structural results…

Let F be a finitely generated field of characteristic zero and \Gamma<GL_n(F) a finitely generated subgroup. For an element g in \Gamma, let Gal(F(g)/ F) be the Galois group of the splitting field of the characteristic polynomial of g over…

This paper studies when a pair of elements in F are the images of the standard generators of F under a self monomorphism.

In this paper we consider Tyler's robust covariance M-estimator under group symmetry constraints. We assume that the covariance matrix is invariant to the conjugation action of a unitary matrix group, referred to as group symmetry. Examples…

A machine developed by the second author produces a rich family of unitary representations of the Thompson groups F,T and V. We use it to give direct proofs of two previously known results. First, we exhibit a unitary representation of V…

We prove a homological stability theorem for families of discrete groups (e.g. mapping class groups, automorphism groups of free groups, braid groups) with coefficients in a sequence of irreducible algebraic representations of arithmetic…

The goal of the paper is to develop a systematic approach to the study of (perhaps degenerate) singularities of integrable systems and their structural stability. As the main tool, we use "hidden" system-preserving torus actions near…

We determine, up to the equivalence of first-order interdefinability, all structures which are first-order definable in the random partial order. It turns out that these structures fall into precisely five equivalence classes. We achieve…

Thompson's groups, which are denoted by $F, T$ and $V$, were introduced by R. Thompson. It is known that they are related to various fields in mathematics. In this paper, we establish that Thompson's groups are regarded as subgroups of…

Working in the soft-element (classical) viewpoint, we introduce \emph{soft bitopological groups}: soft groups endowed with two soft topologies such that the induced topologies on the set of soft elements make the soft-element group into a…

Among the infinite classes of finite simple groups, the most exotic classes are probably the Suzuki groups and the Ree groups. They are "twisted versions" of groups of Lie type, but they cannot be directly obtained as groups of rational…

Suwa investigated the unit group scheme of the group ring associated with a finite flat group scheme and provided a characterization of torsors possessing the normal base property for such schemes. In this paper, we examine the unit group…

We show that a large family of groups is uniformly stable relative to unitary groups equipped with submultiplicative norms, such as the operator, Frobenius, and Schatten $p$-norms. These include lamplighters $\Gamma \wr \Lambda$ where…

The Butcher group is a powerful tool to analyse integration methods for ordinary differential equations, in particular Runge--Kutta methods. Recently, a natural Lie group structure has been constructed for this group. Unfortunately, the…

The Ben Geloun-Rivasseau quantum field theoretical model is the first tensor model shown to be perturbatively renormalizable. We define here an appropriate Hopf algebra describing the combinatorics of this new tensorial renormalization. The…

In Chapter 1 we give the basic background and notations. We also give a new characterization of the Conrad property for orderings. In Chapter 2, we use the new characterization of the Conradian property to give a classification of groups…

Let $X$ be a smooth algebraic variety endowed with an action of a finite group $G$ such that there exists the geometric quotient $\pi_X:X\to X/G$. We characterize rational tensor fields $\tau$ on $X/G$ such that the {\it pull back} of $\tau…

We characterize the combinatorial types of symmetric frameworks in the plane that are minimally generically symmetry-forced infinitesimally rigid when the symmetry group consists of rotations and translations. Along the way, we use tropical…