Related papers: Abels's groups revisited

We establish the mathematical fundamentals for a unified description of curvature, torsion, and non-metricity 2-forms in the way extending the so-called M\"{o}bius representation of the affine group, which is the method to convert the…

We characterize finitely generated torsion-free Kleinian groups for which the real length spectrum (without multiplicities) is discrete.

Long ago, Arad and Herzog (AH) conjectured that, in finite simple groups, the product of two conjugacy classes of length greater than one is never a single conjugacy class. We discuss implications of this conjecture for non-abelian anyons…

We prove that a finite-dimensional omega-categorical group is finite-by-abelian-by-finite and that a finite-dimensional omega-categorical ring is virtually finite-by-null.

A classical theorem of Fritz John allows one to describe a convex body, up to constants, as an ellipsoid. In this article we establish similar descriptions for generalized (i.e. multidimensional) arithmetic progressions in terms of proper…

Let $k$ be a field that is finitely generated over the field of rational numbers and $Br(k)$ the Brauer group of $k$. Let $X$ be an absolutely irreducible smooth projective variety over $k$, let $Br(X)$ be the cohomological…

An abelian group $A$ is said to be cancellable if whenever $A \oplus G$ is isomorphic to $A \oplus H$, $G$ is isomorphic to $H$. We show that the index set of cancellable rank 1 torsion-free abelian groups is $\Pi^0_4$ $m$-complete, showing…

We study the set of all m-tuples $(\lambda(1),...,\lambda(m))$ of possible types of finite abelian p-groups $M_{\lambda(1)}, ..., M_{\lambda(m)}$ for which there exists a long exact sequence $M_{\lambda(1)} \to ... \to M_{\lambda(m)}$. When…

H\"older-Brascamp-Lieb inequalities provide upper bounds for a class of multilinear expressions, in terms of $L^p$ norms of the functions involved. They have been extensively studied for functions defined on Euclidean spaces.…

We study model geometries of finitely generated groups. If a finitely generated group does not contain a non-trivial finite rank free abelian commensurated subgroup, we show any model geometry is dominated by either a symmetric space of…

Many bundle gerbes constructed in practice are either infinite-dimensional, or finite-dimensional but built using submersions that are far from being fibre bundles. Murray and Stevenson proved that gerbes on simply-connected manifolds,…

We prove that certain Fuchsian triangle groups are profinitely rigid in the absolute sense, i.e. each is distinguished from all other finitely generated, residually finite groups by its set of finite quotients. We also develop a method…

The goal of this note is to provide yet another proof of the following theorem of Golod: there exists an infinite finitely generated group $G$ such that every element of $G$ has finite order. Our proof is based on the Nielsen-Schreier index…

We prove that the $p^\infty$-torsion of the transcendental Brauer group of an abelian variety over a finitely generated field of characteristic $p>0$ is bounded. This answers a (variant of a) question asked by Skorobogatov and Zarhin for…

Let $M$ be a covariant coefficient system for a finite group $G$. In this paper we analyze several topological abelian groups, some of them new, whose homotopy groups are isomorphic to the Bredon-Illman $G$-equivariant homology theory with…

It is known from work by H. Abels and P. Abramenko that for a classical Fq-group G of rank n the arithemetic lattice G(Fq[t]) of Fq[t]-rational points is of type Fn-1 provided that q is large enough. We show that the statement is true…

Vl{\u a}du{\c t} characterized in 1999 the set of finite fields $k$ such that all elliptic curves defined over $k$ have a cyclic group of rational points. Under the conjecture of infinitely many Mersenne primes, this set is infinite. In…

In this note, we give a new formula for the number of cyclic subgroups of a finite abelian group. This is based on applying the Burnside's lemma to a certain group action. Also, it generalizes the well-known Menon's identity.

We prove that all finitely generated fully residually free groups (limit groups) have a sequence of finite dimensional unitary representations that `strongly converge' to the regular representation of the group. The corresponding statement…

We study graph products of groups from the viewpoint of measured group theory. We first establish a full measure equivalence classification of graph products of countably infinite groups over finite simple graphs with no transvection and no…