3 papers
math.GR2026
A Möbius function on the centralizer lattice
William Cocke, Mark L. Lewis, Ryan McCulloch
We consider the Möbius function on the poset of element centers and obtain some new results regarding centralizers in a -group.
math.GR2025
Covering by Centralizers
Mark L. Lewis, Ryan McCulloch
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…
math.GR2025
The commuting graph and a graph associated with centralizers
Mark L. Lewis, Ryan McCulloch
Let be a -group. We begin to consider the relationship between the structure of the commuting graph and . We also build a family of groups whose commuting graphs h…