Related papers: Conciseness of compact $R$-analytic groups

It was recently proven that all free and many virtually free verbally closed subgroups are algebraically closed in any group. We establish sufficient conditions for a group that is an extension of a free non-abelian group by a group…

We show that strong approximate lattices in higher-rank semi-simple algebraic groups are arithmetic.

Given a group word $w$ and a group $G$, the set of $w$-values in $G$ is denoted by $G_w$ and the verbal subgroup $w(G)$ is the one generated by $G_w$. In the present paper we consider profinite groups admitting a word $w$ such that the…

We show that every finite-dimensional p-adic Lie group of class C^k admits a C^k-compatible analytic Lie group structure.

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…

We prove that every verbally closed subgroup of a free group $F$ of a finite rank is a retract of $F.$

We prove that affine Coxeter groups are profinitely rigid.

We reduce the classification of finite subgroups in compact Lie groups to that of quasi-simple ones, prove the number of conjugacy classes is finite and each cojugacy class is Zariski closed in mapping space, and classify "strongly…

Some completely positive maps on reduced amalgamated free products of C*-algebras are constructed; these allow a proof that the class of exact unital C*-algebras is closed under taking reduced amalgamated free products. Consequently, the…

We investigate the star-free closure, which associates to a class of languages its closure under Boolean operations and marked concatenation. We prove that the star-free closure of any finite class and of any class of groups languages with…

We prove that in every finitely generated profinite group, every subgroup of finite index is open; this implies that the topology on such groups is determined by the algebraic structure. This is deduced from the main result about finite…

We prove the Gasch\"utz Lemma holds for all metrisable compact groups.

It is shown that any compact semistable quotient (in the sense of Heinzner and Snow) of a normal algebraic variety by a complex reductive Lie group $G$ is a good quotient. This reduces the investigation and classification of such…

We show that every locally compact strictly convex metric group is abelian, thus answering one problem posed by the authors in their earlir paper. To prove this theorem we first construct the isomorphic embeddings of the real line into the…

Answering a question of A. V. Vasil'ev, we show that each finite symmetric (or alternating) group $H$ is a retract of any group containing $H$ as a verbally closed subgroup.

Using the concept of algebraically closed groups, we prove that there is a countable torsion free group with exactly two conjugacy classes.

We prove that existentially closed $CSA$-groups have the independence property. This is done by showing that there exist words having the independence property relatively to the class of torsion-free hyperbolic groups.

Relying on the techniques and ideas from our recent paper [13], we prove several anti-classification results for various rigidity conditions in countable abelian and nilpotent groups. We prove three main theorems: (1) the rigid abelian…

It is proved that, in certain subgroups of direct products of countable groups, the property of being an unconditionally closed set coincides with that of being an algebraic set. In particular, these properties coincide in all Abelian…

We study expressive power of continuous logic in classes of (locally compact) groups. We also describe locally compact groups which are separably categorical structures.