Related papers: A model-theoretic note on the Freiman-Ruzsa theore…

We prove a version of the fundamental theorems of Morse Theory in the setting of finite spaces or partially ordered sets. By using these results we extend Forman's discrete Morse theory to more general cell complexes and derive the…

We present a new fragment of axiomatic set theory for pure sets and for the iteration of power sets within given transitive sets. It turns out that this formal system admits an interesting hierarchy of models with true membership relation…

The Cauchy-Davenport theorem states that for any two nonempty subsets A and B of Z/pZ we have |A+B| >= min{p,|A|+|B|-1}, where A+B:={a+b (mod p) | a in A, b in B}. We generalize this result from Z/pZ to arbitrary finite (including…

We establish new bounds in the Bogolyubov-Ruzsa lemma, demonstrating that if A is a subset of a finite abelian group with density alpha, then 3A-3A contains a Bohr set of rank O(log^2 (2/alpha)) and radius Omega(log^{-2} (2/alpha)). The…

We prove a Freiman-Ruzsa-type theorem valid in an arbitrary nilpotent group. Specifically, we show that a K-approximate subgroup A of an s-step nilpotent group G is contained in a coset nilprogression of rank at most f(K) and cardinality at…

It is shown that for a subset $A\subset\R^n$ that has the global Gabrielov property, a Vitushkin-type estimate holds. Concrete examples are given for sub-level sets of certain classes of functions.

We prove a query complexity variant of the weak polynomial Freiman-Ruzsa conjecture in the following form. For any $\epsilon > 0$, a set $A \subset \mathbb{Z}^d$ with doubling $K$ has a subset of size at least $K^{-\frac{4}{\epsilon}}|A|$…

A Tauberian theorem deduces an asymptotic for the partial sums of a sequence of non-negative real numbers from analytic properties of an associated Dirichlet series. Tauberian theorems appear in a tremendous variety of applications, ranging…

In this note some properties of the sum of element orders of a finite abelian group are studied.

We finish the classification, begun in two earlier papers, of all simple fusion systems over finite nonabelian $p$-groups with an abelian subgroup of index $p$. In particular, this gives many new examples illustrating the enormous variety…

The purpose of this brief note is to sharpen a result of Kepka about the axiomization of the variety of trimedial quasigroups.

We establish a uniform upper estimate for the values of zeta(s)/zeta(s+A), 0<= A, on the critical line (conditionally on the Riemann Hypothesis). We use this to give a variant, purely complex analytic, to Baez-Duarte's proof of a…

We consider abelain subgroups of small index in finite groups. More generally, we consider subgroups such that the product of their index by the index of their centralizer is small.

In this paper, we develop some basic techniques towards the Riemann hypothesis for higher rank non-abelian zeta functions of an integral regular projective curve of genus $g$ over a finite field $\mathbb F_q$. As an application of the…

We obtain non-uniform Berry-Esseen type estimates for several classes of weakly dependent sequences of random variables, including uniformly elliptic inhomogeneous Markov chains, random and time-varying (partially) hyperbolic or expanding…

We point out some limits of the perturbative renormalization group used in statistical mechanics both at and out of equilibrium. We argue that the non perturbative renormalization group formalism is a promising candidate to overcome some of…

We investigate Gabor frames on locally compact abelian groups with time-frequency shifts along non-separable, closed subgroups of the phase space. Density theorems in Gabor analysis state necessary conditions for a Gabor system to be a…

We present some Zermelo-Fraenkel consistency results regarding bi-orderability of groups, as well as a construction of groups with Conradian orders whose every action on metric spaces has bounded orbits. A classical consequence of the…

In this paper we study non-central almost subnormal subgroups of the multiplicative group of a division ring satisfying a non-zero generalized rational identity. The main result generalizes Chiba's theorem on subnormal subgroups. As an…

Szemeredi's regularity lemma is an important tool in graph theory which has applications throughout combinatorics. In this paper we prove an analogue of Szemeredi's regularity lemma in the context of abelian groups and use it to derive some…