Topologies on Smashed Twisted Wreath Products of Metagroups

The Geometry of Twisted Conjugacy Classes in Wreath Products

We give a geometric proof based on recent work of Eskin, Fisher and Whyte that the lamplighter group Ln has infinitely many twisted conjugacy classes for any automorphism φ only when n is divisible by 2 or 3, originally proved by Gonçalves and Wong. We determine when the wreath product G o Z has this same property for several classes of finite groups G, including symmetric groups and some nilpo...

Two results on wreath products

Among the familiar basic facts concerning unrestricted permutational wreath products (sketched in the first few paragraphs of the last section of Cossey, Kegel, and Kov~cs [2]), the Embedding Theorem has the central role. It asserts the existence of an embedding; the proof is a construction which involves arbitrarily chosen coset representatives, with the effect that the embedding constructed m...

On the Iteration of Weak Wreath Products

Based on a study of the 2-category of weak distributive laws, we describe a method of iterating Street’s weak wreath product construction. That is, for any 2-category K and for any non-negative integer n, we introduce 2-categories Wdl(K), of (n + 1)-tuples of monads in K pairwise related by weak distributive laws obeying the Yang-Baxter equation. The first instance Wdl(K) coincides with Mnd(K),...

The Wreath Products

Rooted Wreath Products

We introduce “rooted valuation products” and use them to construct universal Abelian lattice-ordered groups (with prescribed set of components) [CHH] from the more classical theory of [Ha]. The Wreath product construction of [H] and [HMc] generalised the Abelian (lattice-ordered) group ideas to a permutation group setting to respectively give universals for transitive (`-) permutation groups wi...