On the Chermak–Delgado lattice of a finite group

Abstract

By imposing conditions upon the index of a self-centralizing subgroup 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.

Finite Groups With Large Chermak–delgado Lattices

“…It was first introduced by Chermak and Delgado [4] and revisited by Isaacs [5]. In the last few years, there has been a growing interest in understanding this lattice (see [1–3, 6–8, 11–14]). We recall several important properties of the Chermak–Delgado measure: if , then , and if the measures are equal, then ; if , then and ; the maximal member M of is characteristic and ; the minimal member of (called the Chermak–Delgado subgroup of G ) is characteristic, abelian and contains . …”

Finite groups with a certain number of values of the Chermak–Delgado measure

“…In the last years there has been a growing interest in understanding this lattice (see e.g. [3,4,5,6,8,10,11,12,13,15,18,20]). We recall several important properties of the Chermak-Delgado measure that will be used in our paper:…”