Covering by Centralizers
Group Theory
2026-04-08 v2
Abstract
In this paper, we consider covers of finite groups by centralizers of elements. We show that the set of centralizers that are maximal under the partial ordering form a cover of the group. We also show that the set of centralizers that are minimal under the partial ordering form a cover of the group. We show for -groups that are nonabelian -groups that the number of distinct nontrivial centralizers is congruent to modulo .
Cite
@article{arxiv.2512.02211,
title = {Covering by Centralizers},
author = {Mark L. Lewis and Ryan McCulloch},
journal= {arXiv preprint arXiv:2512.02211},
year = {2026}
}