Central products and the Chermak–Delgado lattice

Abstract

The Chermak–Delgado lattice of a finite group is a modular, self-dual sublattice of the lattice of subgroups. We prove that the Chermak–Delgado lattice of a central product contains the product of the Chermak–Delgado lattices of the relevant central factors. Furthermore, we obtain information about heights of elements in the Chermak–Delgado lattice relative to their heights in the Chermak–Delgado lattices of central factors. We also explore how the central product can be used as a tool in investigating Chermak–Delgado lattices.