Related papers: Wreath products of semigroups in universal algebra…

We address the problem of determining the class of self-similar groups, and in particular its closure under restricted direct products. We show that the group $\mathbb Z^{(\omega)}$ is self-similar, that $G^{(\omega)}\rtimes C_2$ is…

We investigate closure results for C-approximable groups, for certain classes C of groups with invariant length functions. In particular we prove, each time for certain (but not necessarily the same) classes C that (i) the direct product of…

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…

A result of Farahat and Higman shows that there is a ``universal'' algebra, $\mathrm{FH}$, interpolating the centres of symmetric group algebras, $Z(\mathbb{Z}S_n)$. We explain that this algebra is isomorphic to $\mathcal{R} \otimes…

We consider a family of Hecke C*-algebras which can be realised as crossed products by semigroups of endomorphisms. We show by dilating representations of the semigroup crossed product that the category of representations of the Hecke…

A notion of \emph{graph-wreath product} is introduced. We obtain sufficient conditions for these products to satisfy the topologically inspired finiteness condition type $\operatorname{F}_n$. Under various additional assumptions we show…

A wreath product is a method to construct an association scheme from two association schemes. We determine the automorphism group of a wreath product. We show a known result that a wreath product is Schurian if and only if both components…

In analogy to the disjoint cycle decomposition in permutation groups, Ore and Specht define a decomposition of elements of the full monomial group and exploit this to describe conjugacy classes and centralisers of elements in the full…

Let $m$ be a positive integer and let $\Omega$ be a finite set. The $m$-closure of $G\le$Sym$(\Omega)$ is the largest permutation group on $\Omega$ having the same orbits as $G$ in its induced action on the Cartesian product $\Omega^m$. The…

In this paper, we describe the relationship between the quasi-component q(G) of a (perfectly) minimal pseudocompact abelian group G and the quasi-component q(\widetilde G) of its completion. Specifically, we characterize the pairs (C,A) of…

Let $G = X \wr H$ be the wreath product of a nontrivial finite group $X$ with $k$ conjugacy classes and a transitive permutation group $H$ of degree $n$ acting on the set of $n$ direct factors of $X^n$. If $H$ is semiprimitive, then $k(G)…

We study generalisations of conjugacy separability in restricted wreath products of groups. We provide an effective upper bound for $\mathcal{C}$-conjugacy separability of a wreath product $A \wr B$ in terms of the $\mathcal{C}$-conjugacy…

A major open problem in the theory of twisted commutative algebras (tca's) is proving noetherianity of finitely generated tca's. For bounded tca's this is easy, in the unbounded case, noetherianity is only known for Sym(Sym^2(C^\infty)) and…

Let $\sigma:A\rightarrow B$ and $\rho:A\rightarrow C$\ be two homomorphisms of noetherian rings such that $B\otimes_{A}C$ is a noetherian ring. we show that if $\sigma$ is a regular (resp. complete intersection, resp. Gorenstein, resp.…

We describe the $C^*$-algebra of an $E$-unitary or strongly 0-$E$-unitary inverse semigroup as the partial crossed product of a commutative $C^*$-algebra by the maximal group image of the inverse semigroup. We give a similar result for the…

We present a survey of our recent research on varieties, generated by wreath products of groups. In particular, the full classification of all cases, when the (cartesian or direct) wreath product of any abelian groups $A$ and $B$ generates…

Wreath products such as Z wr Z are not finitely-presentable yet can occur as subgroups of finitely presented groups. Here we compute the distortion of Z wr Z as a subgroup of Thompson's group F and as a subgroup of Baumslag's metabelian…

We study isometric representations of product systems of correspondences over the semigroup $\mathbb{N}^k$ which are minimal dilations of finite dimensional, fully coisometric representations. We show the existence of a unique minimal…

In this paper we study the complexity of solving orientable quadratic equations in wreath products $A\wr B$ of finitely generated abelian groups. We give a classification of cases (depending on genus and other characteristics of a given…

Wreath products involving symmetric inverse monoids/semigroups/categories arise in many areas of algebra and science, and presentations by generators and relations are crucial tools in such studies. The current paper finds such…