Related papers: The conjugacy problem for Thompson-like groups

Let $G$ be a classical group defined over a finite field. We consider the following fundamental problems concerning conjugacy in $G$: 1. List a representative for each conjugacy class of $G$. 2. Given $x \in G$, describe the centralizer of…

Viewing Dehn's algorithm as a rewriting system, we generalise to allow an alphabet containing letters which do not necessarily represent group elements. This extends the class of groups for which the algorithm solves the word problem to…

We compute invariants of quadratic forms associated to orthogonal hypergeometric groups of degree five. This allows us to determine some commensurabilities between these groups, as well as to say when some thin groups cannot be conjugate to…

For a finite group $G,$ we define the concept of $G$-partial permutation and use it to show that the structure coefficients of the center of the wreath product $G\wr \mathcal{S}_n$ algebra are polynomials in $n$ with non-negative integer…

We compute the higher $\Sigma$-invariants $\Sigma^m(F_{n,\infty})$ of the generalized Thompson groups $F_{n,\infty}$, for all $m,n\ge 2$. This extends the $n=2$ case done by Bieri, Geoghegan and Kochloukova, and the $m=2$ case done by…

Let $G$ be a group. Two elements $x, y$ are said to be {\it $z$-equivalent} if their centralizers are conjugate in $G$. The class equation of $G$ is the partition of $G$ into conjugacy classes. Further decomposition of conjugacy classes…

Denote by $N_{\ell}(n)$ the number of $\ell$-tuples of elements in the symmetric group $S_n$ with commuting components, normalized by the order of $S_n$. In this paper, we prove asymptotic formulas for $N_\ell(n)$. In addition, general…

We provide a new branching rule from the general linear group $GL_{2n}(\mathbb{C})$ to the symplectic group $Sp_{2n}(\mathbb{C})$ by establishing a simple algorithm which gives rise to a bijection from the set of semistandard tableaux of a…

We define half grid diagrams and prove every link is half grid presentable by constructing a canonical half grid pair (which gives rise to a grid diagram of some special type) associated with an element in the oriented Thompson group. We…

We embed Thompson's group $V$ in the mapping class group of a mixing subshift of finite type. Question~6.3 in [Boyle-Chuysurichay, 17] asks whether these mapping class groups are sofic. Our result suggests that this question is difficult to…

We prove that Claas R\"over's Thompson-Grigorchuk simple group $V\mathcal{G}$ has type $F_\infty$. The proof involves constructing two complexes on which $V\mathcal{G}$ acts: a simplicial complex analogous to the Stein complex for $V$, and…

We prove that fundamental groups of non-orientable 3-manifolds have a solvable conjugacy problem, and construct an algorithm. Together with our earlier work on the conjugacy problem in groups on orientable geometrizable 3-manifolds, all…

We consider groups $G$ such that the set $[G,\varphi]=\{g^{-1}g^{\varphi}|g\in G\}$ is a subgroup for every automorphism $\varphi$ of $G$, and we prove that there exists such a group $G$ that is finite and nilpotent of class $n$ for every…

We study a class of generalisations of Thompson's group $V$ arising naturally as topological full groups of purely infinite, minimal groupoids. In the process, we show that the derived subgroup of such a group is 2-generated whenever it is…

The Thompson group $V$, as well as the Brin-Thompson group $2V$, is finitely generated and can be defined as a monoid acting on bitstrings, respectively pairs of bitstrings. Therefore evaluation problems can be defined for $V$ and $2V$. We…

If $\phi$ is an automorphism of a group $G$ and $x,y\in G$, we say that $x$ and $y$ are $\phi$-twisted conjugates if there exists an $z\in G$ such that $y=z.x.\phi(z^{-1})$. This is an equivalence relation. If there are infinitely many…

We analyse for which $n$ there exist in $G=A_n,S_n$ two proper subgroups $H,K$ such that $G$ is the union of the $G$-conjugacy classes of $H$ and $K$.

In this paper, we consider a time independent $C^2$ Hamiltonian, sa\-tisfying the usual hypothesis of the classical Calculus of Variations, on a non-compact connected manifold. Using the Lax-Oleinik semigroup, we give a proof of the…

We study the notion of twisted conjugacy separability (essentially introduced in our previous paper for a proof of twisted version of Burnside-Frobenius theorem) and some related properties. We give examples of groups with and without this…

We analyze the proof by Lehnert and Schweitzer that the word problem of the Thompson group V is co-context-free, and we show that this word problem is the complement of the cyclic closure of a union of reverse deterministic context-free…