Related papers: Presentations for singular wreath products

The rank of a semigroup is the cardinality of a smallest generating set. In this paper we compute the rank of the endomorphism monoid of a non-trivial uniform partition of a finite set, that is, the semigroup of those transformations of a…

The objective of this paper is to study the monoid of all partial transformations of a finite set that preserve a uniform partition. In addition to proving that this monoid is a quotient of a wreath product with respect to a congruence…

Let $\mathbb{C}\mathsf{A}_n = \mathbb{C}[S_2\wr S_2 \wr\cdots \wr S_2]$ be the group algebra of $n$-step iterated wreath product. We prove some structural properties of $\mathsf{A}_n$ such as their centers, centralizers, right and double…

Whiston proved that the maximum size of an irredundant generating set in the symmetric group $S_n$ is $n-1$, and Cameron and Cara characterized all irredundant generating sets of $S_n$ that achieve this size. Our goal is to extend their…

We introduce a new product for permutation groups. It takes as input two permutation groups, M and N, and produces an infinite group M [X] N which carries many of the permutational properties of M. Under mild conditions on M and N the group…

It is shown that membership in rational subsets of wreath products H \wr V with H a finite group and V a virtually free group is decidable. On the other hand, it is shown that there exists a fixed finitely generated submonoid in the wreath…

The full transformation semigroups $\mathcal{T}_n$, where $n\in \mathbb{N}$, consisting of all maps from a set of cardinality $n$ to itself, are arguably the most important family of finite semigroups. This article investigates the…

We study the class of monoids that arise as the submonoid of right units of finitely presented special inverse monoids (SIMs). Gray and Ru\v{s}kuc (2024) gave the first example of a finitely presented SIM whose submonoid of right units does…

We propose an analogue of Solomon's descent theory for the case of a wreath product G ~ S_n, where G is a finite abelian group. Our construction mixes a number of ingredients: Mantaci-Reutenauer algebras, Specht's theory for the…

This paper concerns a class of semigroups that arise as products $US$, associated to what we call `action pairs'. Here $U$ and $S$ are subsemigroups of a common monoid and, roughly speaking, $S$ has an action on the monoid completion $U^1$…

In this article, we initiate the study of the large-scale geometry of permutational wreath products of the form $F\wr_{H/N}H$, where $H$ is finitely presented and where $N$ is a normal subgroup of $H$ satisfying a certain assumption of non…

We investigate a semigroup construction generalising the two-sided wreath product. We develop the foundations of this construction and show that for groups it is isomorphic to the usual wreath product. We also show that it gives a slightly…

We show that the wreath product of two finite symmetric or alternating groups is 2-generated.

The aim of this paper is to investigate whether the class of automaton semigroups is closed under certain semigroup constructions. We prove that the free product of two automaton semigroups that contain left identities is again an automaton…

Based on a study of the 2-category of weak distributive laws, we describe a method of iterating Street's weak wreath product construction. That is, for any 2-category K and for any non-negative integer n, we introduce 2-categories…

We prove that if a finite group $H$ has a generalized involution model, as defined by Bump and Ginzburg, then the wreath product $H \wr S_n$ also has a generalized involution model. This extends the work of Baddeley concerning involution…

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…

Given a finite group $G$ acting on a set $X$ let $\delta_k(G,X)$ denote the proportion of elements in $G$ that have exactly $k$ fixed points in $X$. Let $\mathrm{S}_n$ denote the symmetric group acting on $[n]=\{1,2,\dots,n\}$. For…

We characterize which permutational wreath products W^(X)\rtimes G are finitely presented. This occurs if and only if G and W are finitely presented, G acts on X with finitely generated stabilizers, and with finitely many orbits on the…

We describe an algorithm for computing the complete set of primitive orthogonal idempotents in the centralizer ring of the permutation representation of a wreath product. This set of idempotents determines the decomposition of the…