相关论文: Twisted conjugacy in generalized Thompson groups o…

A new class of groups, the locally finitely determined groups of local similarities on compact ultrametric spaces, is introduced and it is proved that groups in this class have the Haagerup property (that is, they are a-T-menable in the…

Let $S$ be a semigroup. The elements $a,b\in S$ are called primarily conjugate if $a=xy$ and $b=yx$ for certain $x,y\in S$. The relation of conjugacy is defined as the transitive closure of the relation of primary conjugacy. In the case…

We prove that the tree almost automorphism groups admit exactly three commensurability classes of closed commensurated subgroups. Our proof utilizes an independently interesting characterization of subgroups of the tree almost automorphism…

Let K be a p-adic field and let F and G be two formal groups over O_K. We prove that if F and G have infinitely many torsion points in common, then F=G. This follows from a rigidity result: any bounded power series that sends infinitely…

Automorphism groups are intrincate conjugacy invariants for subshifts, which can reveal important features of the dynamical structure of a shift action. One important case is the study of automorphism groups when the underlying subshift has…

We prove that under two natural probabilistic models (studied by Cleary, Elder, Rechnitzer and Taback), the probability that a random pair of elements of Thompson's group $F$ generate the entire group is positive. We also prove that for any…

Let $K$ be a field of characteristic zero, $X$ and $Y$ be smooth $K$-varieties, and let $G$ be a algebraic $K$-group. Given two algebraic morphisms $\varphi:X\rightarrow G$ and $\psi:Y\rightarrow G$, we define their convolution…

We study a family of Thompson-like groups built as rearrangement groups of fractals from [BF19], each acting on a Wa\.zewski dendrite. Each of these is a finitely generated group that is dense in the full group of homeomorphisms of the…

We show that Brin's generalisations $2V$ and $3V$ of the Thompson-Higman group $V$ are of type $FP_\infty$. Our methods also give a new proof that both groups are finitely presented.

We prove that the Brin-Thompson groups sV, also called higher dimensional Thompson's groups, are of type F_\infty for all natural numbers s. This result was previously shown for s up to 3, by considering the action of sV on a naturally…

We determine when two almost automorphisms of a regular tree are conjugate. This is done by combining the classification of conjugacy classes in the automorphism group of a level-homogeneous tree by Gawron, Nekrashevych and Sushchansky and…

In a group $G$, elements $a$ and $b$ are conjugate if there exists $g\in G$ such that $g^{-1} ag=b$. This conjugacy relation, which plays an important role in group theory, can be extended in a natural way to inverse semigroups: for…

In this paper, we compute the {\Sigma}^n(G) and {\Omega}^n(G) invariants when 1 \rightarrow H \rightarrow G \rightarrow K \rightarrow 1 is a short exact sequence of finitely generated groups with K finite. We also give sufficient conditions…

For a finite group G of Lie type and a prime p, we compare the automorphism groups of the fusion and linking systems of G at p with the automorphism group of G itself. When p is the defining characteristic of G, they are all isomorphic,…

Let the Ricci curvature of a compact Riemannian manifold be greater, at every point, than the Lie derivative of the metric with respect to some fixed smooth vector field. It is shown that the fundamental group then has only finitely many…

Let $F_n$ be the free group of rank $n$ with free basis $X=\{x_1,\dots,x_n \}$. A palindrome is a word in $X^{\pm 1}$ that reads the same backwards as forwards. The palindromic automorphism group $\Pi A_n$ of $F_n$ consists of those…

Let $K$ be a complete quasivariety of topological inverse Clifford semigroups, containing all topological semilattices. It is shown that the free topological inverse semigroup $F(X,K)$ of $X$ in the class $K$ is an $R^\infty$-manifold if…

Let F be an infinitely generated free group and R a fully invariant subgroup of F such that (a) R is contained in the commutator subgroup F' of F and (b) the quotient group F/R is residually torsion-free nilpotent. Then the automorphism…

The palindromic automorphism group is a subgroup of the automorphism group $Aut(F_3).$ We establish a necessary and sufficient condition for a matrix in $GL_n(\mathbb{Z})$ representing a palindromic automorphism of $F_n.$ We prove that the…

We study a class of finite groups $G$ which behave similarly to elementary abelian $p$-groups with $p$ prime, that is, there exists a subgroup $N$ such that all elements of $G\setminus N$ are conjugate or inverse-conjugate under $\Aut(G)$.…