We consider the wreath product of two symmetric groups as a group blocks permutations and we study its conjugacy classes. give polynomiality property for structure coefficients center algebras. This allows us to recover an old result Farahat Higman about algebra generalize our recent hyperoctahedral algebra.

Drimbe and Vaes proved an orbit equivalence superrigidity theorem for left-right wreath product actions in the measurable setting. We establish counterpart result topological setting continuous equivalence. This gives us minimal, topologically free that are superrigid. One main ingredient proof is to show cocycle certain generalized full shifts, extending our previous with Chung.

Isometry classes of linear codes can be expressed as orbits under the group action of a wreath product. Some combinatorial and algebraic methods are discussed which can be applied for generating linear codes distributed uniformly at random over all isometry classes.

In this thesis, we construct an algebraic framework for analyzing committee elections. In this framework, module homomorphisms are used to model positional voting procedures. Using the action of the wreath product group S2[Sn] on these modules, we obtain module decompositions which help us to gain an understanding of the module homomorphism. We use these decompositions to construct some interes...

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

We characterize the automorphism groups of quasiprimitive 2-arc-transitive graphs of twisted wreath product type. This is a partial solution for a problem of Praeger regarding quasiprimitive 2-arc transitive graphs. The solution stimulates several further research problems regarding automorphism groups of edge-transitive Cayley graphs and digraphs.

We establish a new group-theoretic realization of the basic representations of the twisted affine and twisted toroidal algebras of ADE types in the same spirit of our new approach to the McKay correspondence. Our vertex operator construction provides a unified description to the character tables for the spin cover of the wreath product of the twisted hyperoctahedral groups and an arbitrary fini...

A result of Farahat and Higman shows that there is a “universal” algebra, FH, interpolating the centres symmetric group algebras, Z(ℤS n ). We explain this algebra isomorphic to ℛ⊗Λ, where ℛ ring integer-valued polynomials Λ functions. Moreover, isomorphism via “evaluation at Jucys–Murphy elements”, which leads character formulae for groups. Then, we generalise wreath products Γ≀S fixed finite ...