Related papers: A product for permutation groups and topological g…

Asymptotic properties of finitely generated subgroups of free groups, and of finite group presentations, can be considered in several fashions, depending on the way these objects are represented and on the distribution assumed on these…

New results on metric ultraproducts of finite simple groups are established. We show that the isomorphism type of a simple metric ultraproduct of groups $X_{n_i}(q)$ ($i\in I$) for $X\in\{{\rm PGL},{\rm PSp},{\rm PGO}^{(\varepsilon)},{\rm…

Let C be a class of groups. We give sufficient conditions ensuring that a free product of residually C groups is again residually C, and analogous conditions are given for locally embeddable into C groups. As a corollary, we obtain that the…

Expanding on previous work of the author, we initiate the model theoretic study of W$^*$-dynamical systems. We axiomatize continuous weight-preserving group actions of $G$ on von Neumann algebras for $G$ a given locally compact Hausdorff…

Many transformation groups on manifolds are simple, but their universal coverings are not. In the present paper, we study the concept of relatively simple group, that is, a group with the maximum proper normal subgroup. We show that many…

In this article, we consider tensor products of unitary representations by irreducible non-unitary finite dimensional representations of topological groups to define a property that is a twisting of Kazhdan's Property (T). We use the…

We introduce two new binary operations with combinatorial species; the arithmetic product and the modified arithmetic product. The arithmetic product gives combinatorial meaning to the product of Dirichlet series and to the Lambert series…

In this paper, we show that there is a net for amenable transformation groups like F{\o}lner net for amenable groups and investigate amenability of a transformation group constructed by semidirect product of groups. We introduce inner…

We consider the question of when sets definable in first-order expansions of groups contain the product of two infinite sets (we refer to this as the "productset property"). We first show that the productset property holds for any definable…

In various classes of infinite groups, we identify groups that are presentable by products, i.e. groups having finite index subgroups which are quotients of products of two commuting infinite subgroups. The classes we discuss here include…

While there has been growing interest for noncommutative spaces in recent times, most examples have been based on the simplest noncommutative algebra: [x_i,x_j]=i theta_{ij}. Here we present new classes of (non-formal) deformed products…

Let $\mathfrak{S}_\infty$ be the infinity permutation group and $\Gamma$ be a separable topological group. The wreath product $\Gamma\wr \mathfrak{S}_\infty$ is the semidirect product $\Gamma^\infty_e \rtimes \mathfrak{S}_\infty$ for the…

We describe the structure, including composition factors and submodule lattices, of cross-characteristic permutation modules for the natural actions of the orthogonal groups $O_{m}^{\pm}(3)$ with $m\geq6$ on nonsingular points of their…

We show that $\mathcal{U}(\mathbb{Z}G)$, the unit group of the integral group ring $\mathbb{Z} G$, either satisfies Kazhdan's property (T) or is, up to commensurability, a non-trivial amalgamated product, in case $G$ is a finite group…

The main theorem is that if K is a finite CW complex with finite fundamental group G and universal cover homotopy equivalent to a product of spheres X, then G acts smoothly and freely on X x S^n for any n greater than or equal to the…

Given a group $G$ and $n\geq 0$, let $W(G,n)$ be the associated iterated wreath product -- unrestricted when $G$ is infinite -- viewed as a permutation group on $G^n$. We prove that the normalizer of $W(G,n)$ in the symmetric group $S(G^n)$…

We define a tensor product for permutative categories and prove a number of key properties. We show that this product makes the 2-category of permutative categories closed symmetric monoidal as a bicategory.

We prove that if a subgroup $H$ of the automorphism group $\mathrm{Aut}(\Sigma^{\mathbb{Z}})$ of a non-trivial full shift acts on points of finite support with a free orbit, then for every finitely-generated abelian group $A$, the abstract…

We present a contribution to the structure theory of locally compact groups. The emphasis is on compactly generated locally compact groups which admit no infinite discrete quotient. It is shown that such a group possesses a characteristic…

Let G be a finite group and let M be a G-manifold. We introduce the concept of generalized orbifold invariants of M/G associated to an arbitrary group Gamma, an arbitrary Gamma-set, and an arbitrary covering space of a connected manifold…