Subgroups of Twisted Wreath Products

Abstract

By determining subdirect products invariant under the action of a regular permutation group of the components we provide a natural motivation for the definition of twisted wreath products. Then—based on papers of R. Baddeley, A. Lucchini, F. B¨orner, and M. Aschbacher—we explain how twisted wreath products play a fundamental role in the problem of representing finite lattices as intervals in subgroup lattices of finite groups.