Wreath product
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Topological and Thermodynamic Entropy Measures for COVID-19 Pandemic through Graph Theory Open
Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has caused the global pandemic, coronavirus disease-2019 (COVID-19) which has resulted in 60.4 million infections and 1.42 million deaths worldwide. Mathematical models as an int…
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Speed of random walks, isoperimetry and compression of finitely generated groups Open
International audience
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Affine Wreath Product Algebras Open
We study the structure and representation theory of affine wreath product algebras and their cyclotomic quotients. These algebras, which appear naturally in Heisenberg categorification, simultaneously unify and generalize many important al…
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Flag-transitive automorphism groups of 2-designs with λ ≥ (r, λ)^2 and an application to symmetric designs Open
Let D be a 2-(v, k, λ) design with λ ≥ (r, λ)2. If G ≤ Aut(D) is flag-transitive, then G cannot be of simple diagonal or twisted wreath product type, and if G is product type then the socle of G has exactly two components and G has rank 3.…
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LOCALLY COMPACT WREATH PRODUCTS Open
Wreath products of nondiscrete locally compact groups are usually not locally compact groups, nor even topological groups. As a substitute introduce a natural extension of the wreath product construction to the setting of locally compact g…
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Smashed and Twisted Wreath Products of Metagroups Open
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.
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Knapsack Problems for Wreath Products Open
In recent years, knapsack problems for (in general non-commutative) groups have attracted attention. In this paper, the knapsack problem for wreath products is studied. It turns out that decidability of knapsack is not preserved under wrea…
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Spectrum, distance spectrum, and Wiener index of wreath products of complete graphs Open
We describe the adjacency matrix and the distance matrix of the wreath product of two complete graphs, and we give an explicit computation of their spectra. As an application, we deduce the spectrum of the transition matrix of the Lampligh…
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Metric Approximations of Wreath Products Open
Given the large class of groups already known to be sofic, there is seemingly a shortfall in results concerning their permanence properties. We address this problem for wreath products, and in particular investigate the behaviour of more g…
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The Derived Subgroups of Sylow 2-Subgroups of the Alternating Group, Commutator Width of Wreath Product of Groups Open
The structure of the commutator subgroup of Sylow 2-subgroups of an alternating group A 2 k is determined. This work continues the previous investigations of me, where minimal generating sets for Sylow 2-subgroups of alternating groups wer…
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Total Distance, Wiener Index and Opportunity Index in Wreath Products of Star Graphs Open
In the last decades much attention has turned towards centrality measures on graphs. The Wiener index and the total distance are key tools to investigate the median vertices, the distance-balanced property and the opportunity index of a gr…
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Haagerup property for wreath products constructed with Thompson's groups Open
Using recent techniques introduced by Jones, we prove that a large family of discrete groups and groupoids have the Haagerup property. In particular, we show that if \Gamma is a discrete group with the Haagerup property, then the permutati…
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Regular left-orders on groups Open
A regular left-order on a finitely generated group G is a total, left-multiplication invariant order on G whose corresponding positive cone is the image of a regular language over the generating set of the group under the evaluation map. W…
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Quantum Affine Wreath Algebras Open
To each symmetric algebra we associate a family of algebras that we call quantum affine wreath algebras . These can be viewed both as symmetric algebra deformations of affine Hecke algebras of type A and as quantum deformations of affine w…
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Matrix wreath products of algebras and embedding theorems Open
We introduce a new construction of matrix wreath products of algebras that is similar to wreath products of groups. We then use it to prove embedding theorems for Jacobson radical, nil, and primitive algebras. In §6, we construct finitely …
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Cayley Automatic Representations of Wreath Products Open
We construct the representations of Cayley graphs of wreath products using finite automata, pushdown automata and nested stack automata. These representations are in accordance with the notion of Cayley automatic groups introduced by Kharl…
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Generalized Cyclotomic Mappings: Switching Between Polynomial, Cyclotomic, and Wreath Product Form Open
This paper is concerned with so-called index $d$ generalized cyclotomic mappings of a finite field $\mathbb{F}_q$, which are functions $\mathbb{F}_q\rightarrow\mathbb{F}_q$ that agree with a suitable monomial function $x\mapsto ax^r$ on ea…
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Boolean Product Polynomials, Schur Positivity, and Chern Plethysm Open
Let $k \leq n$ be positive integers, and let $X_n = (x_1, \dots , x_n)$ be a list of $n$ variables. The Boolean product polynomial $B_{n,k}(X_n)$ is the product of the linear forms $\sum _{i \in S} x_i$, where $S$ ranges over all $k$-eleme…
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Poset models for Weyl group analogs of symmetric functions and Schur functions Open
The `Weyl symmetric functions' studied here naturally generalize classical symmetric (polynomial) functions, and `Weyl bialternants,' sometimes also called Weyl characters, analogize the Schur functions. For this generalization, the underl…
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Subvariety structures in certain product varieties of groups Open
We classify certain cases when the wreath products of distinct pairs of groups generate the same variety. This allows us to investigate the subvarieties of some nilpotent-by-abelian product varieties 𝔘 𝔙 {{\mathfrak{U}}{\mathfrak{V}}…
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On maximum intersecting sets in direct and wreath product of groups Open
For a permutation group G acting on a set V, a subset I of G is said to be an intersecting set if for every pair of elements g,h∈I there exists v∈V such that g(v)=h(v). The intersection density ρ(G) of a transitive permutation group G is t…
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EDT0L solutions to equations in group extensions Open
We show that the class of groups where EDT0L languages can be used to describe solution sets to systems of equations is closed under direct products, wreath products with finite groups, and passing to finite index subgroups. We also add th…
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World Scientific Publishing Open
We show that the unrestricted wreath product of a sofic group by an amenable group is sofic. We use this result to present an alternative proof of the known fact that any group extension with sofic kernel and amenable quotient is again a s…
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Hyperbolic structures on wreath products Open
The study of the poset of hyperbolic structures on a group G was initiated by C. Abbott, S. Balasubramanya and D. Osin, [Hyperbolic structures on groups, Algebr. Geom. Topol. 19 2019, 4, 1747–1835, 10.2140/agt.2019.19.1747]. However, this …
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On matrix wreath products of algebras Open
We introduce a new construction of matrix wreath products of algebras that is similar to the construction of wreath products of groups introduced by L. Kaloujnine and M. Krasner [17]. We then illustrate its usefulness by proving embedding …
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Conjugacy growth series of some wreath products Open
In this paper we consider groups of the form $G\wr L$, where the set of generators naturally extends the sets of generators of $G$ and $L$, and $L$ admits a Cayley graph that is a tree. We show how one can compute the conjugacy growth seri…
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Lamplighter groups, median spaces and Hilbertian geometry Open
From any two median spaces $X$ and $Y$ , we construct a new median space $X \circledast Y$ , referred to as the diadem product of $X$ and $Y$ , and we show that this construction is compatible with wreath products in the following sense: g…
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Metric approximations of unrestricted wreath products when the acting group is amenable Open
We give a simple and unified proof showing that the unrestricted wreath product of a weakly sofic, sofic, linear sofic, or hyperlinear group by an amenable group is weakly sofic, sofic, linear sofic, or hyperlinear, respectively. By means …
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Lamplighter groups, median spaces, and a-T-menability Open
This paper is dedicated to the proof of the following statement: the wreath product of two groups acting metrically properly on median spaces acts metrically properly on some median space we call space of wreaths. As a consequence of this …
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Some properties of Specht modules for the wreath product of symmetric groups Open
We investigate a class of modules for the wreath product Sm wr Sn of two symmetric groups which are analogous to the Specht modules of the symmetric group, and prove a range of properties for these modules which demonstrate this analogy. I…