On the Chermak–Delgado Lattice of a Finite Group

Abstract

By imposing conditions upon the index of a self-centralizing sub-group of a group, and upon the index of the center of the group, we are able to classify the Chermak-Delgado lattice of the group. This is our main result. We use this result to classify the Chermak-Delgado lattices of dicyclic groups and of metabelian p-groups of maximal class.