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