Related papers: Free products of circularly-ordered groups with am…
This paper is devoted to the proof of the property of order separability for free product of free groups with maximal cyclic amalgamated subgroups.
Motivated by the recent result that left-orderability of a group $G$ is intimately connected to circular orderability of direct products $G \times \mathbb{Z}/n\mathbb{Z}$, we provide necessary and sufficient cohomological conditions that…
In this paper, we consider the relation between the group freeness and the amalgamated freeness of crossed product algebras.
We study left orderings on countably generated groups. In particular, we construct left orderings of inductive limits of amalgamated free products by using isolated left orderings of the groups appearing in the inductive system. Moreover,…
We partly generalize the estimate for the rank of intersection of subgroups in free products of groups, proved earlier by S.V.Ivanov and W.Dicks, to the case of free amalgamated products of groups with normal finite amalgamated subgroup. We…
It was proved that for any finite set of elements of a free product of residually finite groups such that no two of them belong to conjugate cyclic subgroups and each of them do not belong to a subgroup which is conjugate a to free factor…
We show that an amalgamated free product $G*_{A}H$ admits a discrete isolated ordering, under some assumptions of $G,H$ and $A$. This generalizes the author's previous construction of isolated orderings, and unlike known constructions of…
This is a translation from Russian of the article by A.A.Vinogradov: On the free product of ordered groups, Mat. Sb. (N.S.), 1949, Volume 25(67), Number 1, 163-168. The main result is that the free product of two ordered groups is…
Let $G$ be the generalized free product of two groups with an amalgamated subgroup. We propose an approach that allows one to use results on the residual $p$-finiteness of $G$ for proving that this generalized free product is residually a…
We show that certain orderable groups admit no isolated left orders. The groups we consider are cyclic amalgamations of a free group with a general orderable group, the HNN extensions of free groups over cyclic subgroups, and a particular…
It is proved that all finitely generated subgroups of generalized free product of two groups are finitely separable provided that free factors have this property and amalgamated subgroups are normal in corresponding factors and satisfy the…
We study finite subgroups of outer automorphisms of free products. We give upper bounds for the orders of these finite subgroups as well as bounds for the orders of individual torsion outer automorphisms under some (necessary) conditions…
Let C be a class of groups. We give sufficient conditions ensuring that a free product of residually C groups is again residually C, and analogous conditions are given for locally embeddable into C groups. As a corollary, we obtain that the…
It has recently been proved that the class of unital exact C*-algebras is closed under taking reduced amalgamated free products. In particular, this implied that the class of exact discrete groups is closed under taking amalgamated free…
We show that no left-ordering on a free product of (left-orderable) groups is isolated. In particular, we show that the space of left-orderings of free product of finitely generated groups is homeomorphic to the Cantor set. With the same…
For a subgroup of a free product of finite groups, we obtain necessary conditions (on its Kurosh decomposition) to be verbally closed.
The far-reaching work of Dahmani-Guirardel-Osin and recent work of Clay-Mangahas-Margalit provide geometric approaches to the study of the normal closure of a subgroup (or a collection of subgroups)in an ambient group $G$. Their work gives…
A conjecture of Dicks and the author on rank of the intersection of factor-free subgroups in free products of groups is proved for the case of left ordered groups.
This paper is devoted to the investigation of the property of order separability for HNN extensions and free products with commutative subgroups. Particularly it was proven that HNN extension of a free group with maximal connected cyclic…
We construct the free products of arbitrary digroups, and thus we solve an open problem of Zhuchok.