English

Groups whose Chermak-Delgado lattice is a subgroup lattice of an elementary abelian $p$-group

Group Theory 2021-07-08 v1

Abstract

The Chermak-Delgado lattice of a finite group GG is a self-dual sublattice of the subgroup lattice of GG. In this paper, we focus on finite groups whose Chermak-Delgado lattice is a subgroup lattice of an elementary abelian pp-group. We prove that such groups are nilpotent of class 22. We also prove that, for any elementary abelian pp-group EE, there exists a finite group GG such that the Chermak-Delgado lattice of GG is a subgroup lattice of EE.

Keywords

Cite

@article{arxiv.2107.03108,
  title  = {Groups whose Chermak-Delgado lattice is a subgroup lattice of an elementary abelian $p$-group},
  author = {Lijian An},
  journal= {arXiv preprint arXiv:2107.03108},
  year   = {2021}
}