English

The Chermak-Delgado Measure as a Map on Posets

Group Theory 2024-02-12 v3

Abstract

The Chermak-Delgado measure of a finite group is a function which assigns to each subgroup a positive integer. In this paper, we give necessary and sufficient conditions for when the Chermak-Delgado measure of a group is actually a map of posets, i.e., a monotone function from the subgroup lattice to the positive integers. We also investigate when the Chermak-Delgado measure, restricted to the centralizers, is increasing.

Keywords

Cite

@article{arxiv.2401.12450,
  title  = {The Chermak-Delgado Measure as a Map on Posets},
  author = {William Cocke and Ryan McCulloch},
  journal= {arXiv preprint arXiv:2401.12450},
  year   = {2024}
}