Related papers: Free wreath products with amalgamation
To a finite group G one can associate a tower of wreath products S_n[G]. It is well known that the graded direct sum of the Grothendieck groups of the categories of finite dimensional complex representations of these groups can be given the…
We investigate a semigroup construction related to the two-sided wreath product. It encompasses a range of known constructions and gives a slightly finer version of the decomposition in the Krohn-Rhodes Theorem, in which the three-element…
Wreath products of non-discrete locally compact groups are usually not locally compact groups, nor even topological groups. We introduce a natural extension of the wreath product construction to the setting of locally compact groups. As an…
In the first part of this series, the authors introduced the quantum wreath product, providing a unified framework that encompasses numerous results previously addressed only through case-by-case analysis. This paper shifts focus to the…
In this paper, we present generalizations of some results on the asymptotic property C for wreath products. Specifically, we prove that certain wreath-like products admit asymptotic property C, thus providing some new examples for further…
A transitive simple subgroup of a finite symmetric group is very rarely contained in a full wreath product in product action. All such simple permutation groups are determined in this paper. This remarkable conclusion is reached after a…
In this paper, we compute (co)homologies of ideal boundaries of free products of geodesic coarsely convex spaces in terms of those of each of the components. The (co)homology theories we consider are, $K$-theory, Alexander-Spanier…
An almost-direct product of free groups is an iterated semidirect product of finitely generated free groups in which the action of the constituent free groups on the homology of one another is trivial. We determine the structure of the…
This work is the first step towards a description of the Gromov boundary of the free factor graph of a free product, with applications to subgroup classification for outer automorphisms. We extend the theory of algebraic laminations dual to…
We show that an amalgamated free product $G*_{A}H$ admits a discrete isolated ordering, under some assumptions of $G,H$ and $A$. This generalizes the author's previous construction of isolated orderings, and unlike known constructions of…
In a previous paper [1] [MR4101040], we initiated a systematic study of semihypergroups and had a thorough discussion about some important analytic and algebraic objects associated to this class of objects. In this paper, we investigate…
Given two unital continuous C*-bundles A and B over the same Hausdorff compact base space X, we study the continuity properties of their different amalgamated free products over C(X).
In this paper, we study operator algebraic properties of the reduced and von Neumann algebraic versions of the free wreath products $\mathbb G \wr_* S_N^+$, where $\mathbb G$ is a compact matrix quantum group. Based on recent result on…
We give a characterisation of quantum automorphism groups of trees. In particular, for every tree, we show how to iteratively construct its quantum automorphism group using free products and free wreath products. This can be considered a…
The Haagerup property for locally compact groups is generalised to the context of locally compact quantum groups, with several equivalent characterisations in terms of the unitary representations and positive-definite functions established.…
Normal subgroups and there properties for finite and infinite iterated wreath products $S_{n_1}\wr \ldots \wr S_{n_m}$, $n, m \in \mathbb{N}$ are founded. The special classes of normal subgroups and there orders are investigated. Special…
We give a partial solution a question of Grigorchuk, Nekrashevych, Sushchanskii and \v{S}uni\'k by giving an algorithm to test whether a finite state element of an infinite iterated (permutational) wreath product $\hat G = \mathbb…
In this article nonassociative metagroups are studied. Different types of smashed products and smashed twisted wreath products are scrutinized. Extensions of central metagroups are studied.
Inspired by constructions of Kova\v{c}evi\'{c}, we introduce the amalgamated free product of circle actions, obtained by blowing up two actions along prescribed orbits and rearranging the inserted intervals. Under natural orbit and index…
We consider the finitely generated groups acting on a regular tree with almost prescribed local action. We show that these groups embed as cocompact irreducible lattices in some locally compact wreath products. This provides examples of…