English

The commuting graph and a graph associated with centralizers

Group Theory 2025-11-18 v1

Abstract

Let GG be a pp-group. We begin to consider the relationship between the structure of the commuting graph and G:Z(G)|G:Z(G)|. We also build a family of groups whose commuting graphs have more than one connected component whose diameter is at least 22. For this, we introduce another graph related to the commuting graph that is associated with centralizers.

Keywords

Cite

@article{arxiv.2511.11926,
  title  = {The commuting graph and a graph associated with centralizers},
  author = {Mark L. Lewis and Ryan McCulloch},
  journal= {arXiv preprint arXiv:2511.11926},
  year   = {2025}
}
R2 v1 2026-07-01T07:38:32.222Z