Related papers: Extentability of Automorphisms of Generic Substruc…

Let G be a simple algebraic group over an algebraically closed field k of characteristic 2. We consider analogues of the Jacobson-Morozov theorem in this setting. More precisely, we classify those nilpotent elements with a simple…

In this short note, we give a complete answer to the question of when the generalised F\o lner sets exhibiting property A can be chosen to be subsets of the space itself. More precisely, we prove that this holds for any discrete metric…

Let G be a free group in a variety of groups, but G is not absolutely free. We prove that the group of automorphisms Aut(G) is linear iff G is a virtually nilpotent group.

Let $\varphi$ be a normal semi-finite faithful weight on a von Neumann algebra $A$,let $(\sigma^\varphi_r)_{r\in{\mathbb R}}$ denote the modular automorphism group of $\varphi$, and let $T\colon A\to A$ be a linear map. We say that $T$…

The Urysohn space is the unique separable metric space that is universal and homogeneous for finite metric spaces, i.e., it embeds any finite metric space any isometry between finite subspaces extends to an isometry of the whole space. We…

Let $K[x,y]$ be the polynomial algebra in two variables over an algebraically closed field $K$. We generalize to the case of any characteristic the result of Furter that over a field of characteristic zero the set of automorphisms $(f,g)$…

We investigate Ramsey expansions, the coherent extension property for partial isometries (EPPA), and the existence of a stationary independence relation for all classes of metrically homogeneous graphs from Cherlin's catalogue. We show…

In this paper, we give new constructions of Urysohn universal ultrametric spaces. We first characterize a Urysohn universal ultrametric subspace of the space of all continuous functions whose images contain the zero, from a zero-dimensional…

A geometric characterization of the structure of the group of automorphisms of an arbitrary Birkhoff-Grothendieck bundle splitting $\bigoplus_{i=1}^{r} \mathcal(m_{i})$ over $\mathbb{C}\mathbb{P}^{1}$ is provided, in terms of its action on…

Suppose that a Lie algebra $L$ admits a finite Frobenius group of automorphisms $FH$ with cyclic kernel $F$ and complement $H$ such that the characteristic of the ground field does not divide $|H|$. It is proved that if the subalgebra…

We give elementary proofs of the following two theorems on automorphisms of a finite group G: (1) An automorphism of G is inner if and only if it extends to an automorphism of every finite group containing G. (2) There exists a finite…

Let $X$ be a smooth, projective, geometrically connected curve over a finite field $\mathbb{F}_q$, and let $G$ be a split semisimple algebraic group over $\mathbb{F}_q$. Its dual group $\hat{G}$ is a split reductive group over $\mathbb{Z}$.…

We prove a theorem that gives a sufficient condition for the full basic automorphism group of a complete Cartan foliation to admit a unique (finite-dimensional) Lie group structure in the category of Cartan foliations. Emphasize that the…

We examine properties of generic automorphisms of the random poset, with the goal of explicitly characterizing them. We associate to each automorphism an auxiliary first-order structure, consisting of the random poset equipped with an…

Tent and Ziegler proved that the automorphism group of the Urysohn sphere is simple and that the automorphism group of the Urysohn space is simple modulo bounded automorphisms. A key component of their proof is the definition of a…

We view ultrametric spaces as two-sorted structures consisting of a set of points and of a linearly ordered set of distances. We call the appropriate notion of embeddings distance-carrying (dc for short). Those are obtained by combining…

Let $S$ be a $p$-subgroup of the $\K$-automorphism group $\aut(\cX)$ of an algebraic curve $\cX$ of genus $\gg\ge 2$ and $p$-rank $\gamma$ defined over an algebraically closed field $\mathbb{K}$ of characteristic $p\geq 3$.In this paper we…

We prove that any continuous mapping $f:E\to Y$ on a completely metrizable subspace $E$ of a perfect paracompact space $X$ can be extended to a Lebesgue class one mapping $g:X\to Y$ (i.e. for every open set $V$ in $Y$ the preimage…

In this paper we prove that the automorphism groups of certain countable generic structures are not amenable. For doing that, we first prove the existence of particular matrices that do not satisfy the convex Ramsey condition. For a pair of…

We investigate conditions for the extendibility of continuous algebra homomorphisms $\phi$ from the Fourier algebra $A(F)$ of a locally compact group $F$ to the Fourier-Stieltjes algebra $B(G)$ of a locally compact group $G$ to maps between…