Related papers: Stable length in stable groups

We prove that a permutation group in which different finite sets have different stabilizers cannot satisfy any group law. For locally compact topological groups with this property we show that almost all finite subsets of the group generate…

Let $G$ be a transitive permutation group on a finite set with solvable point stabiliser and assume that the solvable radical of $G$ is trivial. In 2010, Vdovin conjectured that the base size of $G$ is at most 5. Burness proved this…

We investigate under which conditions the cosmological constant vanishes perturbatively at the one-loop level for heterotic strings on non-supersymmetric toroidal orbifolds. To obtain model-independent results, which do not rely on the…

Inspired by the classical category theorems of Halmos and Rohlin for the discrete measure preserving transformations, we prove analogous results in the abstract setting of unitary and isometric C_0-semigroups on a separable Hilbert space.…

Let $F$ be a global field. Let $G$ be a non trivial finite \'etale tame $F$-group scheme. We define height functions on the set of $G$-torsors over $F,$ which generalize the usual heights such as discriminant. As an analogue of the Malle…

We note a parallel between some ideas of stable model theory and certain topics in finite combinatorics related to the sum-product phenomenon. For a simple linear group G, we show that a finite subset X with |X X \^{-1} X |/ |X| bounded is…

We examine Hilbert-Schmidt stability (HS-stability) of discrete amenable groups from several angles. We give a short, elementary proof that finitely generated nilpotent groups are HS-stable. We investigate the permanence of HS-stability…

We prove rigidity type results on the vanishing of stable (co)homology for modules of finite complete intersection dimension, results which generalize and improve upon known results. We also introduce a notion of pre-rigidity, which…

We prove a structure theorem for stable functions on amenable groups, which extends the arithmetic regularity lemma for stable subsets of finite groups. Given a group $G$, a function $f\colon G\to [-1,1]$ is called stable if the binary…

The paper deals with the long-term behavior of positive operator semigroups on spaces of bounded functions and of signed measures, which have applications to parabolic equations with unbounded coefficients and to stochastic analysis. The…

We show that Haar measures of connected semisimple groups, embedded via a representation into a matrix space, have a homogeneous asymptotic limit when viewed from far away and appropriately rescaled. This is still true if the Haar measure…

We show that Wise's power alternative is stable under certain group constructions, use this to prove the power alternative for new classes of groups, and recover known results from a unified perspective. For groups acting on trees, we…

We study the impact of certain identities and probabilistic identities on the structure of finite groups. More specifically, let $w$ be a nontrivial word in $d$ distinct variables and let $G$ be a finite group for which the word map…

The Deligne-Mumford stable reduction theorem asserts that for a family of stable curves over the punctured disk, after a finite base change, the family can be completed in a unique way to a family of stable curves over the disk. In this…

We prove that in a continuous $\aleph_0$-stable theory every type-definable group is definable. The two main ingredients in the proof are: \begin{enumerate} \item Results concerning Morley ranks (i.e., Cantor-Bendixson ranks) from…

By employing a new strategy we prove that all parabolically induced unitary representations of the Burger-Mozes universal group U(F)^+, with F being primitive, have all their matrix coefficients vanishing at infinity. This generalizes the…

Several well-known open questions (such as: are all groups sofic/hyperlinear?) have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups $\mathrm{Sym}(n)$ (in the sofic case) or the finite…

The conditions for stability of the elements of linear groups over the associative rings with identity and their connection with the stability of rings are analyzed in the article. The stability of rings which are commutative, satisfy the…

We discuss a conjecture of Gromov and Lawson, later modified by Rosenberg, concerning the existence of metrics of positive scalar curvature. It says that a closed spin manifold $M$ of dimension $n\ge 5$ has such a metric if and only if the…

We prove that the second Hochschild cohomology group of the moduli stack of stable $n$-pointed genus $g$ curves vanishes for all but finitely many $(g,n)$.