A note on the Chermak-Delgado lattice of a finite group

TL;DR

This paper characterizes finite groups whose Chermak-Delgado lattice forms a specific interval between the center and the group itself, providing structural insights into such groups.

Contribution

It offers a description of the structure of finite groups with a Chermak-Delgado lattice equal to the interval [G/Z(G)].

Findings

Identifies the structure of groups with Chermak-Delgado lattice as [G/Z(G)]

Provides conditions under which the lattice takes this form

Enhances understanding of the relationship between group centers and Chermak-Delgado lattices

Abstract

In this note we describe the structure of finite groups G whose Chermak-Delgado lattice is the interval [G/Z(G)] = {H \in L(G) \mid Z(G)\leq H\leq G}.