Bases of twisted wreath products

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...

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...

Eigenvalues of Random Wreath Products

Steven N. Evans Department of Statistics #3860, University of California at Berkeley 367 Evans Hall, Berkeley, CA 94720-3860, U.S.A [email protected] Abstract Consider a uniformly chosen element Xn of the n-fold wreath product Γn = G o G o · · · o G, where G is a finite permutation group acting transitively on some set of size s. The eigenvalues of Xn in the natural sn-dimensional permuta...

Wreath Products of Permutation Classes

A permutation class which is closed under pattern involvement may be described in terms of its basis. The wreath product construction X o Y of two permutation classes X and Y is also closed, and we investigate classes Y with the property that, for any finitely based class X, the wreath product X o Y is also finitely based.