Related papers: On $T$-sequences and characterized subgroups

Peterzil and Steinhorn proved that if a group $G$ definable in an $o$-minimal structure is not definably compact, then $G$ contains a definable torsion-free subgroup of dimension one. We prove here a $p$-adic analogue of the…

The main goal of the article is to study the Pontryagin duality for Abelian $s$- and $sb$-groups. Let $G$ be an infinite Abelian group and $X$ be the dual group of the discrete group $G_d$. We show that a dense subgroup $H$ of $X$ is…

Let $S$ be a semiabelian variety over an algebraically closed field, and let $X$ be an irreducible subvariety not contained in a coset of a proper algebraic subgroup of $S$. We show that the number of irreducible components of $[n]^{-1}(X)$…

Let $G$ be a connected linear algebraic group over a number field $K$, let $\Gamma$ be a finitely generated Zariski dense subgroup of $G(K)$ and let $Z\subseteq G(K)$ be a thin set, in the sense of Serre. We prove that, if…

We study finite groups $G$ with the property that for any subgroup $M$ maximal in $G$ whose order is divisible by all the prime divisors of $|G|$, $M$ is supersolvable. We show that any nonabelian simple group can occur as a composition…

A topological group $G$ is extremely amenable if every continuous action of $G$ on a compact space has a fixed point. Using the concentration of measure techniques developed by Gromov and Milman, we prove that the group of automorphisms of…

Let $H$ be a transfer Krull monoid over a finite ablian group $G$ (for example, rings of integers, holomorphy rings in algebraic function fields, and regular congruence monoids in these domains). Then each nonunit $a \in H$ can be written…

In this paper, we prove a series of results on group embeddings in groups with a small number of generators. We show that each finitely generated group $G$ lying in a variety ${\mathcal M}$ can be embedded in a $4$-generated group $H \in…

A Polish group $G$ is called a group of quasi-invariance or a QI-group, if there exist a locally compact group $X$ and a probability measure $\mu$ on $X$ such that 1) there exists a continuous monomorphism of $G$ to $X$, and 2) for each…

Let $n>0$ be an integer and $\mathcal{X}$ be a class of groups. We say that a group $G$ satisfies the condition $(\mathcal{X},n)$ whenever in every subset with $n+1$ elements of $G$ there exist distinct elements $x,y$ such that $<x,y>$ is…

Let $U$ be a unipotent group which is graded in the sense that it has an extension $H$ by the multiplicative group of the complex numbers such that all the weights of the adjoint action on the Lie algebra of $U$ are strictly positive. We…

An $S$-ring (Schur ring) is called separable with respect to a class of $S$-rings $\mathcal{K}$ if it is determined up to isomorphism in $\mathcal{K}$ only by the tensor of its structure constants. An abelian group is said to be separable…

We show that if G is a finite group then no chain of modular elements in its subgroup lattice L(G) is longer than a chief series. Also, we show that if G is a nonsolvable finite group then every maximal chain in L(G) has length at least two…

Suppose $(X,\sigma)$ is a subshift, $P_X(n)$ is the word complexity function of $X$, and ${\rm Aut}(X)$ is the group of automorphisms of $X$. We show that if $P_X(n)=o(n^2/\log^2 n)$, then ${\rm Aut}(X)$ is amenable (as a countable,…

Let $(X,L)$ be a polarized variety over a number field. We suppose that $L$ is an hermitian line bundle. Let $M$ be a non compact Riemann Surface and $U\subset M$ be a relatively compact open set. Let $\varphi:M\to X({\Bbb C})$ be a…

Given a $T$-sequence on a countable abelian group $G$, we prove that there exists $2^{2^{|G|}}$ Hausdorff group topologies in which this sequence converges to $0$. This answers a question posed in Intern. J. Math. Math. Sci. {\bf 24}(3)…

For a smooth quasi-affine variety $X$, the affine closure $\overline{T^*X} := \text{Spec}(\mathbb{K}[T^*X])$ contains $T^*X$ as an open subset, and its smooth locus carries a symplectic structure. A natural question is whether…

For a countable ultrahomogeneous graph G let P(G) denote the collection of domains of subgraphs of G isomorphic to G. The order types of maximal chains in the set P(G) U {\o} ordered by the inclusion are characterized as: (I) the order…

Given a permutation group $G$, the derangement graph of $G$ is defined with vertex set $G$, where two elements $x$ and $y$ are adjacent if and only if $xy^{-1}$ is a derangement. We establish that, if $G$ is transitive with degree exceeding…

The notion of locally quasi-convex abelian group, introduce by Vilenkin, is extended to maximally almost-periodic non-necessarily abelian groups. For that purpose, we look at certain bornologies that can be defined on the set…