In this paper and its sequel we study arrays of coupled identical cells that possess a ‘global’ symmetry group G, and in which the cells possess their own ‘internal’ symmetry group L. We focus on general existence conditions for symmetry-breaking steady-state and Hopf bifurcations. The global and internal symmetries can combine in two quite different ways, depending on how the internal symmetri...

The semidirect product of pseudovarieties of semigroups with an order-computable pseudovariety is investigated. The essential tool is the natural representation of the corresponding relatively free profinite semigroups and how it transforms implicit signatures. Several results concerning the behavior of the operation with respect to various kinds of tameness properties are obtained as applicati...

Given natural numbers m and n, we define a deflation map from the characters of the symmetric group Smn to the characters of Sn. This map is defined by first restricting a character of Smn to the wreath product Sm oSn, and then taking the sum of the irreducible constituents of the restricted character on which the base group Sm × · · · × Sm acts trivially. We prove a combinatorial formula which...