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.

Keywords:

• Chermak–Delgado measure
• Chermak–Delgado lattice
• Chermak–Delgado subgroup
• subgroup lattice
• (generalized) dicyclic group
• metabelian group

MSC 2000:

• Primary 20D30
• Secondary 20D60
• 20D99

Acknowledgments

The authors are grateful to the reviewer for its remarks which improve the previous version of the article.

Disclosure statement

No potential conflict of interest was reported by the authors.