相关论文: A note on Automorphisms of the Affine Cremona Grou…

For any right-angled Artin group $A_{\Gamma}$, Charney--Stambaugh--Vogtmann showed that the subgroup $U^0(A_{\Gamma}) \leq\text{Out}(A_{\Gamma})$ generated by Whitehead automorphisms and inversions acts properly and cocompactly on a…

The action of a finite group $G$ on a subshift of finite type $X$ is called free, if every point has trivial stabilizer, and it is called inert, if the induced action on the dimension group of $X$ is trivial. We show that any two free inert…

We consider a normal complete rational variety with a torus action of complexity one. In the main results, we determine the roots of the automorphism group and give an explicit description of the root system of its semisimple part. The…

By [6], a minimal group $G$ is called $z$-minimal if $G/Z(G)$ is minimal. In this paper, we present the $z$-Minimality Criterion for dense subgroups with some applications to topological matrix groups. For a locally compact group $G$, let…

We consider rational projective homogeneous varieties over an algebraically closed field of positive characteristic, namely quotients of a semi-simple group by a possibly non-reduced parabolic subgroup. We determine the group scheme…

It is a well-known fact that every group $G$ has a presentation of the form $G = F/R$, where $F$ is a free group and $R$ the kernel of the natural epimorphism from $F$ onto $G$. Driven by the desire to obtain a similar presentation of the…

Let $G$ be a countable monoid and let $A$ be an Artinian group (resp. an Artinian module). Let $\Sigma \subset A^G$ be a closed subshift which is also a subgroup (resp. a submodule) of $A^G$. Suppose that $\Gamma$ is a finitely generated…

Given two automorphisms of a group $G$, one is interested in knowing whether they are conjugate in the automorphism group of $G$, or in the abstract commensurator of $G$, and how these two properties may differ. When $G$ is the fundamental…

There are various results in the literature which are part of the general philosophy that a finite group for which a certain parameter (for example, the number of conjugacy classes or the maximum number of elements inverted, squared or…

We offer a criterion for showing that the automorphism group of an ultrahomogeneous structure is topologically 2-generated and even has a cyclically dense conjugacy class. We then show how finite topological rank of the automorphism group…

We give a simple set of generators and relations for the Cremona group of the plane. Namely, we show that the Cremona group is the amalgamated product of the de Jonqui\`eres group with the group of automorphisms of the plane, divided by one…

Let $X$ be a smooth projective curve over an algebraically closed field $k$. Let $\mathcal{G}$ be a Bruhat-Tits group scheme on $X$ which is generically semi-simple and trivial. We show that the \'etale fundamental group of the moduli stack…

For a reductive group G and a finite order Cartan-type automorphism \iota of G, we construct an eigenvariety parameterizing \iota-invariant cuspidal Hecke eigensystems of G. In particular, for G = Gln, we prove, any self-dual cuspidal Hecke…

Let $k = \mathbb{F}_p$ or $\mathbb{Z}_p$ (or finite extensions of these). Let $G$ be a $p$-valuable group, and form its completed group algebra $kG$. By analysing the conjugation action of $G$ on itself, we prove two structural results.…

We construct explicitly a family of proper subgroups of the tame automorphism group of affine three-space (in any characteristic) which are generated by the affine subgroup and a non-affine tame automorphism. One important corollary is the…

Let $d > 1$, and let $(X,\alpha)$ and $(Y,\beta)$ be two zero-entropy ${\mathbb{Z}}^d$-actions on compact abelian groups by $d$ commuting automorphisms. We show that if all lower rank subactions of $\alpha$ and $\beta$ have completely…

Let $G = H\times A$ be a group, where $H$ is a purely non-abelian subgroup of $G$ and $A$ is a non-trivial abelian factor of $G$. Then, for $n \geq 2$, we show that there exists an isomorphism $\phi : Aut_{Z(G)}^{\gamma_{n}(G)}(G)…

Given a countable group $G$ splitting as a free product $G=G_1\ast\dots\ast G_k\ast F_N$, we establish classification results for subgroups of the group $Out(G,\mathcal{F})$ of all outer automorphisms of $G$ that preserve the conjugacy…

For a hyperbolic toral automorphism, we construct a profinite completion of an isomorphic copy of the homoclinic group of its right action using isomorphic copies of the periodic data of its left action. The resulting profinite group has a…

Let $X$ be a variety of dimension $n$, and let $\mathrm{Aut}(X)$ be its automorphism group. When $X$ is quasi-affine, we prove that a solvable subgroup of $\mathrm{Aut}(X)$ that is generated by an irreducible family of automorphisms…