Central Products and the Chermak-Delgado Lattice
Group Theory
2024-08-02 v3
Abstract
The Chermak-Delgado lattice of a finite group is a modular, self-dual sublattice of the lattice of subgroups. We prove that the Chermak-Delgado lattice of a central product contains the product of the Chermak-Delgado lattices of the relevant central factors. Furthermore, we obtain information about heights of elements in the Chermak-Delgado lattice relative to their heights in the Chermak-Delgado lattices of central factors. We also explore how the central product can be used as a tool in investigating Chermak-Delgado lattices.
Keywords
Cite
@article{arxiv.2206.12758,
title = {Central Products and the Chermak-Delgado Lattice},
author = {William Cocke and Ryan McCulloch},
journal= {arXiv preprint arXiv:2206.12758},
year = {2024}
}