Finite generation of iterated wreath products

Finite Generation and Presentability of Wreath Products of Monoids

This paper gives necessary and sufficient conditions for the restricted wreath product of two monoids to be finitely generated or finitely presented.

On Finite Generation and Other Finiteness Conditions for Wreath Products of Semigroups

Commutativity Degrees of Wreath Products of Finite Abelian Groups

We compute commutativity degrees of wreath products A o B of finite abelian groups A and B . When B is fixed of order n the asymptotic commutativity degree of such wreath products is 1/n2. This answers a generalized version of a question posed by P. Lescot. As byproducts of our formula we compute the number of conjugacy classes in such wreath products, and obtain an interesting elementary numbe...

Representation Zeta Functions of Wreath Products with Finite Groups

Let G be a group which has a finite number hn(G) of irreducible linear representations in GLn(C) for all n ≥ 1. Let ζ(G, s) = P∞ n=1 hn(G)n −s be its representation zeta function. First, in case G = H oXQ is a permutational wreath product with respect to a permutation group Q on a finite set X, we establish a formula for ζ(G, s) in terms of the zeta functions of H and of subgroups of Q, and of ...

WREATH PRODUCTS AND REPRESENTATIONS OF p-LOCAL FINITE GROUPS

Given two finite p-local finite groups and a fusion preserving morphism between their Sylow subgroups, we study the question of extending it to a continuous map between the classifying spaces. The results depend on the construction of the wreath product of p-local finite groups which is also used to study p-local permutation representations.