Related papers: Free products of circularly-ordered groups with am…
Stallings folding theory is modified, using double coset representatives, and to applied to the study of subgroups of amalgamated products of finite rank free groups. As a first application the subgroup membership problem for such groups is…
We construct a generalized version for the free product of unital C*-algebras over a family of unital C*-subalgebras, starting from the group-analogue. When all the subalgebras are the same, we recover the free product with amalgamation…
The paper deals with the problem posed by Katz and Morris whether the free product with amalgamation of any Hausdorff topological groups is Hausdorff, the negative solution of which (even for the particular case of a closed amalgamated…
In this paper, we construct countably many isolated circular orders on the free products $G = F_{2n} \ast \mathbb{Z}_{m_1} \ast \cdots \ast \mathbb{Z}_{m_k}$ of cyclic groups. Moreover, we prove that these isolated circular orders are not…
Free products of two residually finite groups with amalgamated retracts are considered. It is proved that a cyclic subgroup of such a group is not finitely separable if, and only if, it is conjugated with a subgroup of a free factor which…
Given a group $G = H_1 \ast_A H_2$ which is the free product of two finitely generated groups $H_1$ and $H_2$ with amalgamation over a cyclic subgroup $A$ which is malnormal in $G$, we study relations between the structure of its subgroups…
We present amalgamated free products satisfying coupling rigidity with respect to the automorphism group of the associated Bass-Serre tree. As an application, we obtain orbit equivalence rigidity for amalgamated free products of mapping…
We prove that the amalgamated free product of two free groups of rank two over a common cyclic subgroup, admits an amenable, faithful, transitive action on an infinite countable set. We also show that any finite index subgroup admits such…
Let $D$ be a division ring of fractions of a crossed product $F[G,\eta,\alpha]$ where $F$ is a skew field and $G$ is a group with Conradian left-order $\leq$. For $D$ we introduce the notion of freeness with respect to $\leq$ and show that…
We give a geometric proof of a well known theorem that describes splittings of a free group as an amalgamated product or HNN extension over the integers. The argument generalizes to give a similar description of splittings of a virtually…
In this paper we study residual solvability of the amalgamated product of two finitely generated free groups, in the case of doubles. We find conditions where this kind of structure is residually solvable, and show that in general this is…
We show that the class of amalgamated free products of two free groups over a cyclic subgroup admits amenable, faithful and transitive actions on infinite countable sets. This work generalizes the results on such actions for doubles of free…
This paper establishes necessary and sufficient conditions for the products of freely independent unitary operators to converge in distribution to the uniform law on the unit circle.
We show that every irreducible toroidal integer homology sphere graph manifold has a left-orderable fundamental group. This is established by way of a specialization of a result due to Bludov and Glass for the almagamated products that…
Let $G$ be a free product of two groups with amalgamated subgroup, $\pi$ be either the set of all prime numbers or the one-element set \{$p$\} for some prime number $p$. Denote by $\Sigma$ the family of all cyclic subgroups of group $G$,…
We prove a bi-ordered version of Rivas' result for free products of left-order groups. Namely, we show that a free product of bi-ordered groups does not admit isolated bi-ordering. Our method relies on the dynamical realization of…
We give a new method to construct isolated left orderings of groups whose positive cones are finitely generated. Our construction uses an amalgamated free product of two groups having an isolated ordering. We construct a lot of new examples…
We calculate the rank gradient and p-gradient of free products, free products with amalgamation over an amenable subgroup, and HNN extensions with an amenable associated subgroup. The notion of cost is used to compute the rank gradient of…
We show that the conjugacy problem is solvable in [finitely generated free]-by-cyclic groups, by using a result of O. Maslakova that one can algorithmically find generating sets for the fixed subgroups of free group automorphisms, and one…
We investigate accessible subgroups of a profinite group $G$, i.e. subgroups $H$ appearing as vertex groups in a graph of profinite groups decomposition of $G$ with finite edge groups. We prove that any accessible subgroup $H \leq G$ arises…