Related papers: Expansivity and Roquette Groups

Let $G$ be a dp-minimal group; we prove some consequences of several different hypotheses on $G$. First, if $G$ is torsion-free, then it is abelian. Second, if $G$ admits a distal f-generic type, then it is virtually nilpotent; we prove…

For every finite $p$-group $G_p$ that is non-cyclic and non-quaternion and every positive integer $\ell\neq p$ that is greater than $2$, we prove the first non-trivial bound on $\ell$-torsion in class group of every $G_p$-extension. More…

Let $S$ be a Dedekind scheme, $X$ a connected $S$-scheme locally of finite type and $x\in X(S)$ a section. The aim of the present paper is to establish the existence of the fundamental group scheme of $X$, when $X$ has reduced fibers or…

Let R be a regular local ring. Let G be a reductive R-group scheme. A conjecture of Grothendieck and Serre predicts that a principal G-bundle over R is trivial if it is trivial over the quotient field of R. The conjecture is known when R…

A linear algebraic group G defined over a field k is called special if every G-torsor over every field extension of k is trivial. In 1958 Grothendieck classified special groups in the case where the base field is algebraically closed. In…

Every countable group that does not contain a finitely generated subgroup of exponential growth imbeds in a finitely generated group of subexponential growth. This produces in particular the first examples of groups of subexponential growth…

For a given variety of groups $\X$, we develop a systematic theory of $\CSX$-groups and $\XT$-groups, extending ideas proposed in \cite{Shah}. We analyze the interplay between these classes, describe their structural properties, and examine…

Unlike the classical Brauer group of a field, the Brauer-Grothendieck group of a singular scheme need not be torsion. We show that there exist integral normal projective surfaces over a large field of positive characteristic with…

Let ${\cal N}_{c_1,...,c_t}$ be the variety of polynilpotent groups of class row $(c_1,...,c_t)$. In this paper, first, we show that a polynilpotent group $G$ of class row $(c_1,...,c_t)$ has no any ${\cal N}_{c_1,...,c_t,c_{t+1}}$-covering…

Let Q denote a smooth manifold acted upon smoothly by a Lie group G. The G-action lifts to an action on the total space T of the cotangent bundle of Q and hence on the standard symplectic Poisson algebra of smooth functions on T. The…

We present an explicit construction for the central extension of the group $\Map(X, G)$ where $X$ is a compact manifold and $G$ is a Lie group. If $X$ is a complex curve we obtain a simple construction of the extension by the Picard variety…

In this article we prove that the numerical Grothendieck group of every smooth proper dg category is invariant under primary field extensions, and also that the mod-n algebraic K-theory of every dg category is invariant under extensions of…

We construct box spaces of a free group that do not coarsely embed into a Hilbert space, but do not contain coarsely embedded expanders. We do this by considering two sequences of subgroups of the free group: one which gives rise to a box…

Building on previous results concerning hyperbolicity of groups of Fibonacci type, we give an almost complete classification of the (non-elementary) hyperbolic groups within this class. We are unable to determine the hyperbolicity status of…

We obtain a local central limit theorem for cocycles associated with a class of non abelian and non compact group extensions of Gibbs Markov maps. This class consists of multidimensional infinite dihedral groups. Unlike in the set up of the…

Let R be a discrete valuation ring of unequal characteristic with fraction field K which contains a primitive p^2-th root of unity. Let X be a faithfully flat R-scheme and G be a finite abstract group. Let us consider a G-torsor Y_K\to X_K…

We show that if $G$ is a sufficiently saturated stable group of finite weight with no infinite, infinite-index, chains of definable subgroups, then $G$ is superstable of finite $U$-rank. Combined with recent work of Palacin and Sklinos, we…

It is conjectured that irreducible representations of symmetric groups have no non-trivial self-extension over fields of odd characteristic. We improve on partial results showing evidence of this conjecture.

For a finite smooth algebraic group $F$ over a field $k$ and a smooth algebraic group $\bar G$ over the separable closure of $k$, we define the notion of $F$-kernel in $\bar G$ and we associate to it a set of nonabelian 2-cohomology. We use…

Let $G$ be a Garside group endowed with the generating set $\mathcal{S}$ of non-trivial simple elements, and let $H$ be a parabolic subgroup of $G$. We determine a transversal $T$ of $H$ in $G$ such that each $\theta \in T$ is of minimal…