Maximal complements in wreath products

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...

Maximal complements in finite groups

Let G be a finite group with a non-abelian minimal normal subgroup N which is a direct product of the simple group X. The maximal subgroups of G which complement N and their conjugacy classes are parametrised in terms of certain homomorphisms taking values in AutX and satisfying particular conditions.

Coupled Cells: Wreath Products and Direct Products

In this note we discuss the structure of systems of coupled cells (which we view as systems of ordinary differential equations) where symmetries of the system are obtained through the group G of global permutations of the cells and the group L of local internal symmetries of the dynamics in each cell. We show that even when the cells are assumed to be identical with identical coupling, the way ...

Wreath Products in the Unit Group of Modular Group Algebras of 2-groups of Maximal Class

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 the group G. MSC2000: Primary 16S34, 20C05; Secondary 16U60