Related papers: Group extensions with infinite conjugacy classes

We associate to each finite presentation of a group G a compact CW-complex that is a 3-manifold in the complement of a point, and whose fundamental group is isomorphic to G. We use this complex to define a notion of genus for G and give…

The action of any group on itself by conjugation and the corresponding conjugacy relation play an important role in group theory. There have been several attempts to extend the notion of conjugacy to semigroups. In this paper, we present a…

We give a simple definition of property T for discrete quantum groups. We prove the basic expected properties: discrete quantum groups with property T are finitely generated and unimodular. Moreover we show that, for "I.C.C." discrete…

In this paper we prove that for each dimension $n$ there are only finitely many isomorphism classes of pairs of groups $(\Gamma,\mathrm{N})$ such that $\Gamma$ is an $n$-dimensional crystallographic group and $\mathrm{N}$ is a normal…

A countable discrete group $\Gamma$ is said to have the relative ISR-property if for every non-trivial normal subgroup $N\trianglelefteq\Gamma$ and every von Neumann subalgebra $\mathcal{M}\subseteq L(\Gamma)$ invariant under conjugation by…

In this paper we prove that the general version, F(N) of the Thompson group is inner amenable. As a consequence we generalize a result of P.Jolissaint. To do so, we prove first that F(N) together with a normal subgroup are i.c.c (infinite…

Let ${\cal C}$ be a nonempty class of finite groups closed under taking subgroups, homomorphic images and extensions. A subgroup $H$ of an abstract residually ${\cal C}$ group $R$ is said to be conjugacy ${\cal C}$-distinguished if whenever…

In this paper we prove that whenever $G$ is hyperbolic relative to a family of exact, ressidually finite subgroups $\{H_1, \ldots, H_n\}$, the corresponding von Neumann algebra $\mathcal L(G)$ is solid relative to the family of subalgebras…

It has been shown by Madden that there are only finitely many quadratic extensions of k(x), k a finite field, in which the ideal class group has exponent two and the infinity place of k(x) ramifies. We give a characterization of such fields…

We say that a group $G$ has Bergman's property (the property of universality of finite width) if for every generating set $X$ of $G$ with $X=X^{-1}$ we have that $G=X^k$ for some natural number $k.$ The property is named after George…

In this short note we construct two countable, infinite conjugacy class groups which admit free, ergodic, probability measure preserving orbit equivalent actions, but whose group von Neumann algebras are not (stably) isomorphic.

Given a 2-manifold, a fundamental question to ask is which groups can be realized as the isometry group of a Riemannan metric of constant curvature on the manifold. In this paper, we give a nearly complete classification of such groups for…

We prove that the notion of relative property (T) (or rigidity) for inclusions of finite von Neumann algebras defined in [Po1] is equivalent to a weaker property, in which no ``continuity constants'' are required. The proof is by…

We will introduce a family $\Gamma_\beta, 1 < \beta \in {\mathbb{R}}$ of infinite non-amenable discrete groups as an interpolation of the Higman-Thompson groups $V_n, 1 < n \in {\mathbb{N}}$ by using the topological full groups of the…

In this paper we expand on previous results, studying the extent to which one can detect fusion in certain finite groups $\Gamma$, from information about the universal deformation rings of absolutely irreducible…

In this short note, we classify pairs of conjugacy classes of the symmetric group such that any non-linear irreducible character of the symmetric group vanishes on at least one of them.

We prove that infinite Galois extensions of number fields with Galois group of finite exponent have the Northcott property. The main novelty of our approach lies in the application of a theorem of Segal on profinite groups.

We study qualitative properties of the group von Neumann algebra of a Baumslag-Solitar group. Namely, we prove that, in the non-amenable and {ICC} case, the associated ${\rm II}_1$ factor is prime, not solid, and does not have any Cartan…

Let G be a classical group over an algebraically closed field of characteristic 2 and let C be an elliptic conjugacy class in the Weyl group. In a previous paper the first named author associated to C a unipotent conjugacy class \Phi(C) in…

Let $G$ be a finite non-abelian simple group, $C$ a non-identity conjugacy class of $G$, and $\Gamma_C$ the Cayley graph of $G$ based on $C \cup C^{-1}$. Our main result shows that in any such graph, there is an involution at bounded…