Related papers: The Wreath Product of Two Sofic Groups is Sofic

An example of an extension of a completely simple semigroup U by a group H is given which cannot be embedded into the wreath product of U by H. On the other hand, every central extension of U by H is shown to be embeddable in the wreath…

In this paper we construct finite dimensional representations of the wreath product symplectic reflection algebra H(k,c,N,G) of rank N attached to a finite subgroup G of SL(2,C) (here k is a number and c a class function on the set of…

A group $G$ is integrable if it is isomorphic to the derived subgroup of a group $H$; that is, if $H'\simeq G$, and in this case $H$ is an integral of $G$. If $G$ is a subgroup of $U$, we say that $G$ is integrable within $U$ if $G=H'$ for…

This thesis aims to serve as an introduction to the theory of quasitilings for amenable groups. In order to showcase the power of this theory, we focus on the study of the Sofic L\"uck Approximation Conjecture, which can be proven for…

We study the effects of subgroup distortion in the wreath products A wr Z, where A is finitely generated abelian. We show that every finitely generated subgroup of A wr Z has distortion function equivalent to some polynomial. Moreover, for…

Given a sequence of $(G_i)_{i \in \N}$ of finite transitive groups of degree $n_i$, let $W_\infty$ be the inverse limit of the iterated permutational wreath products of the first m groups. We prove that $W_\infty$ is (topologically)…

The wreath product W(r,n) of the cyclic group of order r and the symmetric group S_n acts on the corresponding projective hyperplane complement, and on its wonderful compactification as defined by De Concini and Procesi. We give a formula…

In this paper we study the classifying spaces of graph products of simplicial groups and connected Hopf algebras over a field, and show that they can be uniformly treated under the framework of polyhedral products. It turns out that these…

We construct a sofic approximation of $\mathbb F_2\times\mathbb F_2$ that is not essentially a "branched cover" of a sofic approximation by homomorphisms. This answers a question of L. Bowen.

We characterize permutational wreath products with Property (FA). For instance, the standard wreath product A wr B of two nontrivial countable groups A,B, has Property (FA) if and only if B has Property (FA) and A is a finitely generated…

We introduce a new matrix product, that we call the wreath product of matrices. The name is inspired by the analogous product for graphs, and the following important correspondence is proven: the wreath product of the adjacency matrices of…

This note extends some results of a previous paper (math.RT/0403250) about finite dimensional representations of the wreath product symplectic reflection algebra H(k,c,N,G) of rank N attached to a finite subgroup G of SL(2,C) (here k is a…

We prove that if a Cartesian product of alternating groups is topologically finitely generated, then it is the profinite completion of a finitely generated residually finite group. The same holds for Cartesian producs of other simple groups…

We describe how the SgpDec computer algebra package can be used for composing and decomposing permutation groups and transformation semigroups hierarchically by directly constructing substructures of wreath products, the so called cascade…

It is known that the notion of a transitive subgroup of a permutation group $P$ extends naturally to the subsets of $P$. We study transitive subsets of the wreath product $G \wr S_n$, where $G$ is a finite abelian group. This includes the…

It is proved that if $G=G_1*_{G_3}G_2$ is free product of probability measure preserving $s$-regular ergodic discrete groupoids amalgamated over an amenable subgroupoid $G_3$, then the sofic dimension $s(G)$ satisfies the equality \[…

Reidemeister (or twisted conjugacy) classes are considered in restricted wreath products of the form $G\wr \mathbb{Z}^k$, where $G$ is a finite group. For an automorphism $\varphi$ of finite order (supposed to be the same for the torsion…

We construct a localic groupoid $\mathbb{G}_{KH}$ such that for any locale $X$ the category of compact Hausdorff locales in the topos of sheaves over $X$ is equivalent to a category whose objects are principal $\mathbb{G}_{KH}$-bundles over…

Connectivity is a homotopy invariant property of a separable C*-algebra A which has three important consequences: absence of nontrivial projections, quasidiagonality and realization of the Kasparov group KK(A,B) as homotopy classes of…

The holomorph of a discrete group $G$ is the universal semi-direct product of $G$. In chapter 1 we describe why it is an interesting object and state main results. In chapter 2 we recall the classical definition of the holomorph as well as…