Related papers: The Wreath Product of Two Sofic Groups is Sofic

Wreath products involving symmetric inverse monoids/semigroups/categories arise in many areas of algebra and science, and presentations by generators and relations are crucial tools in such studies. The current paper finds such…

The irreducible spin character values of the wreath products of the hyperoctahedral groups with an arbitrary finite group are determined.

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…

Given a tensor category $\mathcal{C}$ over an algebraically closed field of characteristic zero, we may form the wreath product category $\mathcal{W}_n(\mathcal{C})$. It was shown in \cite{Ryba} that the Grothendieck rings of these wreath…

Horocyclic products are a well-studied class of metric spaces that provide models for various solvable Lie groups, Baumslag-Solitar groups, and Lamplighter groups. Let $G$ act geometrically on a horocyclic product $X \bowtie Y$ of…

Let G be a finite group and let H be a subgroup of G. The Chermak-Delgado measure of H with respect to G is the product of the order of H with the order of the centralizer of H. Originally described by A. Chermak and A. Delgado, the…

We affirm most open cases of a conjecture that first appeared in Alspach et al. (1987) which stipulates that the wreath (lexicographic) product of two hamiltonian decomposable directed graphs is also hamiltonian decomposable. Specifically,…

We provide elementary proofs of the Nielsen-Schreier Theorem and the Kurosh Subgroup Theorem via wreath products. Our proofs are diagrammatic in nature and work simultaneously in the abstract and profinite categories. A new proof that open…

Let G be a finite group and cd(G) denote the set of complex irreducible character degrees of G. In this paper, we prove that if G is a finite group and H is an almost simple group whose socle is a sporadic simple group H0 such that cd(G) =…

Let $X(G)=GC$ be a group, where $G$ is a semi dihedral group and $C$ is a cyclic group such that $G\cap C=1$. In this paper, $X(G)$ will be characterized.

A group $G$ with conjugation operation is a rack. We call such racks \emph{group racks}. In this paper we study finite group racks via their subrack lattices. Heckenberger, Shareshian, and Welker proved that the isomorphism type of the…

The irreducible character values of the spin wreath products of the symmetric group and an arbitrary finite group are completely determined.

Consider the Grothendieck group of finite type projective modular representations of the symmetric groups on n letters, or more generally, of its wreath product with a finite group. They form a graded group, with a product defined using…

We define a subgroup of the universal sofic group, obtained as the normaliser of a separable abelian subalgebra. This subgroup can be obtained as an extension by the group of automorphisms on a standard probability space. We show that each…

Let $(G_n,X_n)$ be a sequence of finite transitive permutation groups with uniformly bounded number of generators. We prove that the infinitely iterated permutational wreath product $...\wr G_2\wr G_1$ is topologically finitely generated if…

We consider the wreath product of two symmetric groups as a group of blocks permutations and we study its conjugacy classes. We give a polynomiality property for the structure coefficients of the center of the wreath product of symmetric…

For a finite group G one may consider the associated tower S_n[G] of wreath product groups. Zelevinsky associates to such a tower a positive self-adjoint Hopf algebra (PSH-algebra) R(G) as the infinite direct sum of the Grothendieck groups…

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…

Given an edge-independent random graph G(n,p), we determine various facts about the cohomology of graph products of groups for the graph G(n,p). In particular, the random graph product of a sequence of finite groups is a rational duality…

The Farrell-Jones Fibered Isomorphism Conjecture for the stable topological pseudoisotopy theory has been proved for several classes of groups. For example for discrete subgroups of Lie groups, virtually poly-infinite cyclic groups, Artin…