Related papers: Generators and relations for wreath products
We show that, for SU(2) generators of arbitrary dimension $D$, there exist identities that express the completely symmetric product of $D$ matrices in terms of completely symmetric products of fewer number of matrices. We also indicate why…
We examine the geometry of the Cayley graph of the lamplighter group with respect to the generating set rising from its interpretation as an automata group due to Grigorchuk and Zuk. We find some metric behavior with respect to this…
This is a rather personal introductory outline of an interesting class of geometric, resp. graph- and group-theoretical structures. After an introductive section about their genesis, the general construction of horocyclic products is…
We generalize two bijections due to Garsia and Gessel to compute the generating functions of the two vector statistics $(\des_G, \maj,\ell_G, \col)$ and $(\des_G, \ides_G, \maj, \imaj, \col, \icol)$ over the wreath product of a symmetric…
We introduce a notion of partition wreath product of a finite group by a partition quantum group, a construction motivated on the one hand by classical wreath products and on the other hand by the free wreath product of J. Bichon. We…
In this chapter, we discuss normal generators for mapping class groups of surfaces. Especially, we focus on the relation between normal generation of a mapping class with its asymptotic translation lengths on the Teichm\"uller space and the…
The structure of Terwilliger algebras of wreath products by thin schemes or one-class schemes was studied in [A. Hanaki, K. Kim, Y. Maekawa, Terwilliger algebras of direct and wreath products of association schemes, J. Algebra 343 (2011)…
The sister of Eisenstein-Picard modular group was described in [8]. In this paper we give a similar definition of the sister of the Euclidean-Picard modular group and find its generators by using a geometric method.
In this note we study a family of algebras with one parameter defined by generators and relations. The set of generators contains the generators of the usual braids algebra, and another set of generators which is interpreted as ties between…
We give a monoid presentation in terms of generators and defining relations for the partial analogue of the finite dual inverse symmetric monoid.
The rank of a finite semigroup is the smallest number of elements required to generate the semigroup. A formula is given for the rank of an arbitrary (non necessarily regular) Rees matrix semigroup over a group. The formula is expressed in…
We start an analysis of geometric properties of a structure relative to a reduct. In particular, we look at definability of groups and fields in this context. In the relatively one-based case, every definable group is isogenous to a…
In this article the investigation of Sylows p-subgroups of ${{A}_{n}}$ and ${{S}_{n}}$, which was started in article of U. Dmitruk, V. Suschansky "Structure of 2-sylow subgroup of symmetric and alternating group" and article of…
We give a presentation by generators and relations of the group $U_4(\mathbb{Z}[1/\sqrt{2},i])$ of unitary $4\times 4$ matrices with entries in the ring $\mathbb{Z}[1/\sqrt{2},i]$. This is motivated by the problem of exact synthesis for the…
We present a full description of the Bieri-Neumann-Strebel invariant of restricted permutational wreath products of groups. We also give partial results about the 2-dimensional homotopical invariant of such groups. These results may be…
For a sequence of uniformly bounded, degenerate semigroups on a Hilbert space, we compare various types of convergences to a limit semigroup. Among others, we show that convergence of the semigroups, or of the resolvents of the generators,…
For a finitely generated regular wreath product, the metric is known, but its computation can be an NP-complete problem. Also, it is not known for the nonregular case. In this article, a metric estimate is defined for regular wreath…
In the study of Fuchsian groups, it is a nontrivial problem to determine a set of generators. Using a dynamical approach we construct for any cocompact arithmetic Fuchsian group a fundamental region in $\mathbf{SL}_2(\mathbb{R})$ from which…
We prove necessary and sufficient conditions for when graph wreath products are residually finite, generalising known results for the permutational wreath product and free product cases.
This paper classifies the derivations of group algebras in terms of the generators and defining relations of the group. If $RG$ is a group ring, where $R$ is commutative and $S$ is a set of generators of $G$ then necessary and sufficient…