We consider the wreath product of two symmetric groups as a group of blocks permutations and we study its conjugacy classes. We give a polynomiality property for the structure coefficients of the center of the wreath product of symmetric group algebras. This allows us to recover an old result of Farahat and Higman about the polynomiality of the structure coefficients of the center of the symmetric group algebra and to generalize our recent result about the polynomiality property of the structure coefficients of the center of the hyperoctahedral group algebra.
- Centers of finite groups algebras
- Structure coefficients
- Symmetric groups
- Wreath products
ASJC Scopus subject areas
- Algebra and Number Theory
- Discrete Mathematics and Combinatorics