Related papers: A Wreath Product Approach to Classical Subgroup Th…

We define and study a notion of free wreath product with amalgamation for compact quantum groups. These objects were already introduced in the case of duals of discrete groups under the name "free wreath products of pairs" in a previous…

We show that independent Haar-random elements in a super strongly fractal branch profinite group generate a free subgroup acting freely on the boundary of the tree. This improves a previous result of Ab\'ert (2005) for weakly branch…

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…

By a construction of Vaughan Jones, the bipartite graph $\Gamma(A)$ associated with the natural inclusion of $\mathbb C$ inside a finite-dimensional $C^*$-algebra $A$ gives rise to a planar algebra $\mathcal P^{\Gamma(A)}$. We prove that…

In this paper the authors introduce a new notion called the quantum wreath product, which is the algebra $B \wr_Q \mathcal{H}(d)$ produced from a given algebra $B$, a positive integer $d$, and a choice $Q=(R,S,\rho,\sigma)$ of parameters.…

We study the unit group of the modular group algebra KG, where G is a 2-group of maximal class. We prove that the unit group of KG possesses a section isomorphic to the wreath product of a group of order two with the commutator subgroup of…

In this paper, we construct a rigid concrete $C^*$-tensor category whose associated compact quantum group, reconstructed via Woronowicz--Tannaka--Krein duality, is the free wreath product of classical groups.

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…

In this paper we define and develop the theory of the cohomology of a profinite group relative to a collection of closed subgroups. Having made the relevant definitions we establish a robust theory of cup products and use this theory to…

We establish a Bruhat decomposition indexed by the wreath product $\Sigma_m\wr \Sigma_d$ between two symmetric groups -- note that $\Sigma_m\wr \Sigma_d$ is not a Coxeter group in general. We show that such a decomposition affords a…

We study the pro-$p$ Iwahori-Hecke algebra and its Gelfand-Graev modules for the $p$-adic general linear group and its metaplectic covers. We develop the theory of quantum wreath products of skew polynomial type and use it to provide…

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…

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 ${\mathfrak U}{\mathfrak V}$ with the…

By a [$K$-]approximate subring of a ring we mean an additively symmetric subset $X$ such that $X \cdot X \cup (X + X)$ is covered by finitely many [resp.\ $K$] additive translates of $X$. We prove a structure theorem for finite approximate…

Consider the generalized iterated wreath product $S_{r_1}\wr \ldots \wr S_{r_k}$ of symmetric groups. We give a complete description of the traversal for the generalized iterated wreath product. We also prove an existence of a bijection…

We give a formulation of the Nielsen-Schreier theorem (subgroups of free groups are free) in homotopy type theory using the presentation of groups as pointed connected 1-truncated types. We show the special case of finite index subgroups…

We prove that the reduced Kurosh rank of the intersection of two subgroups $H$ and $K$ of a free product of right-orderable groups is bounded above by the product of the reduced Kurosh ranks of $H$ and $K$. In particular, taking the…

Groups with a large $p$-subgroup, $p$ a prime, include almost all of the groups of Lie type in characteristic $p$ and so the study of such groups adds to our understanding of the finite simple groups. In this article we study a special…

We present a new proof, which is independent of the finite simple group classification and applies also to infinite groups, that quasiprimitive permutation groups of simple diagonal type cannot be embedded into wreath products in product…

Coset geometries are incidence geometries constructed from a group $G$ and a system of subgroups $(G_i)_{i \in I}$ of subgroups of $G$. For any algebraic group operation, it is then natural to wonder whether it can be extended to the…