Related papers: Some characterizations of Howson PC-groups

We show that if 2^{aleph_0} Cohen reals are added to the universe, then for every reduced non-free torsion-free abelian group A of cardinality less than the continuum, there is a prime p so that Ext_p(A, Z) not= 0. In particular if it is…

It is shown that a necessary condition for an abstract group G to be the full automorphism group of a Hamiltonian cycle system is that G has odd order or it is either binary, or the affine linear group AGL(1; p) with p prime. We show that…

A beautifully simple free generating set for the commutator subgroup of a free group was constructed by Tomaszewski. We give a new geometric proof of his theorem, and show how to give a similar free generating set for the commutator…

A group obtained from a nontrivial group by adding one generator and one relator which is a proper power of a word in which the exponent-sum of the additional generator is one contains the free square of the initial group and almost always…

We introduce the notion of residual finiteness for categories. In analogy with the group-theoretic setting, we prove that free categories and finitely generated subcategories of finite-dimensional vector spaces are residually finite.…

We show that a Fell bundle B = {B_t}_{t \in F}, over an arbitrary free group F, is amenable, whenever it is orthogonal (in the sense that B_x^* B_y = 0, if x and y are distinct generators of F) and semi-saturated (in the sense that B_{ts}…

We prove that every finitely generated, residually finite group $G$ embeds into a finitely generated perfect branch group $\Gamma$ such that many properties of $G$ are preserved under this embedding. Among those are the properties of being…

The conjecture that semi-p-abelian groups is strongly semi-p-abelian is flase for p=3.And it's true for metabelian semi-p-abelian groups.

We show that all finitely generated free-by-cyclic groups are conjugacy separable: if a finitely generated group $G$ surjects onto $\mathbb{Z}$ with free kernel, then for every pair of non-conjugate elements $g,h\in G$, there exists a…

Integrability conditions for systems of bosons or fermions with seniority conserving hamiltonians are derived. The conditions are shown to be invariant under a large class of transformations of the interaction matrix elements. Previously…

The main result of the paper is that if $A$ is an abelian variety over a subfield $F$ of ${\bold C}$, and $A$ has purely multiplicative reduction at a discrete valuation of $F$, then the Hodge group of $A$ is semisimple. Further, we give…

Given a countable group $G$, we develop a method to construct an overgroup $H$ that is finitely generated, highly transitive and mixed identity free. Our construction can be controlled to ensure that some fundamental group theoretic…

We study the commensurators of free groups and free pro-$p$ groups, as well as certain subgroups of these. We prove that the commensurator $Comm(F)$ of a non-abelian free group of finite rank $F$ is not virtually simple, answering a…

It is well known that a nontrivial commutator in a free group is never a proper power. We prove a theorem that generalizes this fact and has several worthwhile corollaries. For example, an equation $[ x_1, y_1] \ldots [ x_k, y_k] = z^n$,…

We characterize supramenable groups in terms of existence of invariant probability measures for partial actions on compact Hausdorff spaces and existence of tracial states on partial crossed products. These characterizations show that, in…

In the context of finite tensor products of Hilbert spaces, we prove that similarity of a tensor product of operator semigroups to a contraction semigroup is equivalent to the corresponding similarity for each factor, after an appropriate…

Wick polynomials and Wick products are studied in the context of non-commutative probability theory. It is shown that free, boolean and conditionally free Wick polynomials can be defined and related through the action of the group of…

This arXived paper has two independant parts, that are improved and corrected versions of different parts of a single paper once named "On equations in relatively hyperbolic groups". The first part is entitled "Existential questions in…

The paper gives a general condition on permutations, condition under which a semicircular matrix is free independent, or asymptotically free independent from the semicircular matrix obtained by permuting its entries. In particular, it is…

We present a characterization of cotorsion-free abelian groups in terms of homomorphisms from fundamental groups of Peano continua, which aligns naturally with the generalization of slenderness to non-abelian groups. In the process, we…