Related papers: A Measurable-Group-Theoretic Solution to von Neuma…

We study graph products of groups from the viewpoint of measured group theory. We first establish a full measure equivalence classification of graph products of countably infinite groups over finite simple graphs with no transvection and no…

We show that free Burnside groups of sufficiently large odd exponent are non--amenable in a certain strong sense, more precisely, their left regular representations are isolated from the trivial representation uniformly on finite generating…

In this paper we prove that every non-central subnormal subgroup of the multiplicative group of a weakly locally finite division ring contains free non-cyclic subgroups.

The free product of an arbitrary pair of finite hyperfinite von Neumann algebras is examined, and the result is determined to be the direct sum of a finite dimensional algebra and an interpolated free group factor $L(\freeF_r)$. The finite…

We use language theory to study the rational subset problem for groups and monoids. We show that the decidability of this problem is preserved under graph of groups constructions with finite edge groups. In particular, it passes through…

We construct, in locally compact, second countable, amenable groups, sets with large density that fail to have certain combinatorial properties. For the property of being a shift of a set of measurable recurrence we show that this is…

A (discrete) group is called amenable whenever there exists a finitely additive right invariant probablity measure on it. For Thompson's group $F$ the problem whether it is amenable is a long-standing open question. We consider presentation…

We establish a general criterion for the finite presentability of subdirect products of groups and use this to characterize finitely presented residually free groups. We prove that, for all $n\in\mathbb{N}$, a residually free group is of…

To solve problems of Gilbert Baumslag and Hanna Neumann, posed in the 1960's, we construct a nontrivial variety of groups all of whose noncyclic free groups are non-hopfian.

It is shown that a nontrivial normal subgroup $N$ of a group $G$ is a free factor of the $N$'s normal closure in the $G$'s free product with arbitrary nontrivial groups.

The groups distinguish their von Neumann algebras, in the case when these are factors.

We introduce a wide class of countable groups, called properly proximal, which contains all non-amenable bi-exact groups, all non-elementary convergence groups, and all lattices in non-compact semi-simple Lie groups, but excludes all inner…

For any right-angled Artin group, we show that its outer automorphism group contains either a finite-index nilpotent subgroup or a nonabelian free subgroup. This is a weak Tits alternative theorem. We find a criterion on the defining graph…

We show that any countably generated von Neumann algebra with specified normal faithful state can arise as the tail algebra of a quantum exchangeable sequence of noncommutative random variables. We also characterize the cases when the state…

We obtain a homological characterisation of virtually free-by-cyclic groups among groups that are hyperbolic and virtually compact special. As a consequence, we show that many groups known to be coherent actually possess the stronger…

Let $\Gamma$ be a countable group that admits an essential measurable splitting (for instance, any group measure equivalent to a free product of nontrivial groups). We show: (1) for any two nontrivial countable groups $B$ and $C$ that are…

The main objective of this paper is the following two results. (1) There exists a computable bi-orderable group that does not have a computable bi-ordering; (2) There exists a bi-orderable, two-generated recursively presented solvable group…

We introduce the notion of proper proximality for finite von Neumann algebras, which naturally extends the notion of proper proximality for groups. Apart from the group von Neumann algebras of properly proximal groups, we provide a number…

We prove that the normalizer of any diffuse amenable subalgebra of a free group factor $L(\Bbb F_r)$ generates an amenable von Neumann subalgebra. Moreover, any II$_1$ factor of the form $Q \vt L(\Bbb F_r) $, with $Q$ an arbitrary subfactor…

Let $(M, \varphi) = (M_1, \varphi_1) \ast (M_2, \varphi_2)$ be the free product of any $\sigma$-finite von Neumann algebras endowed with any faithful normal states. We show that whenever $Q \subset M$ is a von Neumann subalgebra with…