Related papers: Hopfian combinatorial wreath products
The generalized wreath product of symmetric association schemes was introduced by R.A.Bailey in the European Journal of Combinatorics 27 (2006) 428-435. It is recognized as a unification of both the wreath product and the direct product of…
We give a general construction of rings graded by the conjugacy classes of a finite group. Some examples of our construction are the Hochschild cohomology ring of a finite group algebra, the Grothendieck ring of the Drinfel'd double of a…
It is known that the notion of a transitive subgroup of a permutation group $P$ extends naturally to the subsets of $P$. We study transitive subsets of the wreath product $G \wr S_n$, where $G$ is a finite abelian group. This includes the…
An arrangement of hyperplanes is called formal, if the relations between the hyperplanes are generated by relations in codimension 2. Formality is not a combinatorial property, raising the question for a characterization for combinatorial…
Let I be a finite partially ordered set and let (Sym({\Delta}i),{\Delta}i)i be a sequence of symmetric groups indexed by I. Construct the generalised wreath product (F, {\Delta}) on this sequence of permutation groups. We determine the…
This tutorial is intended to give an accessible introduction to Hopf algebras. The mathematical context is that of representation theory, and we also illustrate the structures with examples taken from combinatorics and quantum physics,…
In [F. Caselli, Involutory reflection groups and their models, J. Algebra 24 (2010), 370--393] it is constructed a uniform Gelfand model for all non-exceptional irreducible complex reflection groups which are involutory. This model can be…
Reidemeister (or twisted conjugacy) classes are considered in restricted wreath products of the form $G\wr \mathbb{Z}^k$, where $G$ is a finite group. For an automorphism $\varphi$ of finite order (supposed to be the same for the torsion…
We explicitly describe the Albanese morphism of a hyperelliptic variety, i.e., the quotient $X$ of an abelian variety $A$ by a finite group $G$ acting freely and not only by translations, by giving a description of the Albanese variety and…
We characterise the group property of being with infinite conjugacy classes for wreath products of groups
We investigate one question regarding bicrossed products of finite groups which we believe has the potential of being approachable for other classes of algebraic objects (algebras, Hopf algebras). The problem is to classify the groups that…
We study the effects of subgroup distortion in the wreath products A wr Z, where A is finitely generated abelian. We show that every finitely generated subgroup of A wr Z has distortion function equivalent to some polynomial. Moreover, for…
Let $A$ be a Hopf algebra in a braided category $\cal C$. Crossed modules over $A$ are introduced and studied as objects with both module and comodule structures satisfying a compatibility condition. The category $\DY{\cal C}^A_A$ of…
Continuing recent studies of both the hereditary and super properties of certain classes of Abelian groups, we explore in-depth what is the situation in the quite large class consisting of directly finite Abelian groups. Trying to connect…
We show that two natural and a priori unrelated structures encapsulate the same data, namely certain commutative and associative product structures and a class of superintegrable Hamiltonian systems. More precisely, consider a Euclidean…
In this paper we begin the systematic study of group equations with abelian predicates in the main classes of groups where solving equations is possible. We extend the line of work on word equations with length constraints, and more…
The main object of study of the present paper is the group $\au_n$ of \emph{unimodular automorphisms} of $\com^n$. Taking $\au_n$ as a working example, our intention was to develop an approach (or rather an edifice) which allows one to…
We study normal finite abelian covers of smooth varieties. In particular we establish combinatorial conditions so that a normal finite abelian cover of a smooth variety is Gorenstein or locally complete intersection.
In the category of abelian groups, Pareigis constructed a Hopf ring whose comodules are differential graded abelian groups. We show that this Hopf ring can be obtained by combining grading and differential Hopf rings using semidirect…
Let VB$_n$ be the virtual braid group on $n$ strands and let $\mathfrak{S}_n$ be the symmetric group on $n$ letters. Let $n,m \in \mathbb{N}$ such that $n \ge 5$, $m \ge 2$ and $n \ge m$. We determine all possible homomorphisms from VB$_n$…