Related papers: Strongly topologically orderable gyrogroups with a…

Let $G$ be an infinite compact group. We prove that for every cardinal $\kappa$ between the density and the weight of $G$, there exists a dense subgroup of $G$ of density $\kappa$.

Let G be a locally compact Hausdorff group in which every element is of finite order, and let P(G) denote the class of all regular probability measures on G. In this note, it is observed that a characterization of algebraically regular…

For any topological group $G$ the dual object $\hat G$ is defined as the set of equivalence classes of irreducible unitary representations of $G$ equipped with the Fell topology. If $G$ is compact, $\hat G$ is discrete, and we investigate…

We investigate some properties of the $p$-elements of a profinite group $G$. We prove that if $p$ is odd and the probability that a randomly chosen element of $G$ is a $p$-element is positive, then $G$ contains an open prosolvable subgroup.…

A subgroup $H$ of a finite group $G$ is called submodular in $G$, if we can connect $H$ with $G$ by a chain of subgroups, each of which is modular (in the sense of Kurosh) in the next. If a group $G$ is supersoluble and every Sylow subgroup…

Let $\mathcal C$ be a class of $T_1$ topological semigroups, containing all Hausdorff zero-dimensional topological semigroups. A semigroup $X$ is $\mathcal C$-$closed$ if $X$ is closed in any topological semigroup $Y\in\mathcal C$ that…

A group $G$ is called subgroup conjugacy separable (abbreviated as SCS), if any two finitely generated and non-conjugate subgroups of $G$ remain non-conjugate in some finite quotient of $G$. We prove that free groups and the fundamental…

Given a definably compact group G in a saturated o-minimal structure, there is a canonical homomorphism from G to a compact real Lie group F(G). We establish a similar result for the (o-mininimal) universal cover of a definably compact…

We study the problem of realizing families of subgroups as the set of stabilizers of configurations from a subshift of finite type (SFT). This problem generalizes both the existence of strongly and weakly aperiodic SFTs. We show that a…

A group $G$ is integrable if it is isomorphic to the derived subgroup of a group $H$; that is, if $H'\simeq G$, and in this case $H$ is an integral of $G$. If $G$ is a subgroup of $U$, we say that $G$ is integrable within $U$ if $G=H'$ for…

A semigroup $T$ is called Taimanov if $T$ contains two distinct elements $0,\infty$ such that $xy=\infty$ for any distinct points $x,y\in T\setminus\{0,\infty\}$ and $xy=0$ in all other cases. We prove that any Taimanov semigroup $T$ has…

Let X be a coherent configuration associated with a transitive group G. In terms of the intersection numbers of X, a necessary condition for the point stabilizer of G to be a TI-subgroup, is established. Furthermore, under this condition, X…

A discrete group $\Gamma$ is called exact if the reduced group C*-algebra ${C_{\lambda}}^{*}(\Gamma)$ is exact as C*-algebras, and a discrete group $\Lambda$ is called residually exact if every nonunital element $g \in \Lambda$ admits a…

We study adequate subgroups of $GL_n$ over a finite field. This notion is useful in the study of automorphy lifting theorems. In particular, we give a sufficient condition for a subgroup to be adequate.

We introduce the notion of graphical discreteness to group theory. A finitely generated group is graphically discrete if whenever it acts geometrically on a locally finite graph, the automorphism group of the graph is compact-by-discrete.…

In this note we prove the following results: $\bullet$ If a finitely presented group $G$ admits a strongly aperiodic SFT, then $G$ has decidable word problem. More generally, for f.g. groups that are not recursively presented, there exists…

Let $P$ be a simplex in $S^n$ and $G_P$ be a group generated by the reflections with respect to the facets of $P$. We are interested in the case when the group $G_P$ is discrete. In this case we say that $G$ generates the discrete…

Let $\phi: G \rightarrow H$ be a group homomorphism such that $H$ is a totally disconnected locally compact (t.d.l.c.) group and the image of $\phi$ is dense. We show that all such homomorphisms arise as completions of $G$ with respect to…

Distributive subsets of the group of all invertible continuous binary operations on a topological space are considered, and it is proved that the subgroups generated by them are also distributive. A criterion for the distributivity of a…

Let $G$ be a group and let $K$ be a commensurated subgroup of $G$. Then there is a totally disconnected, locally compact (t.d.l.c.) group $\hat{G}_K$ that contains the profinite completion of $K$ as an open compact subgroup and also…