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- Argonne National LaboratoryUS410 papers
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33 papers · 1 filter
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…
A characterization of GVZ groups in terms of fully ramified characters
Shawn T. Burkett, Mark L. Lewis
In this paper, we obtain a characterization of GVZ-groups in terms of commutators and monolithic quotients. This characterization is based on counting formulas due to Gallagher.
The Cyclic Graph of a Z-group
David G. Costanzo, Mark L. Lewis, Stefano Schmidt +2
For a group , we define a graph by letting be the set of vertices and by drawing an edge between distinct elements if and o…
The cyclic graph (deleted enhanced power graph) of a direct product
David G. Costanzo, Mark L. Lewis, Stefano Schmidt +2
Let be a finite group. Define a graph on the set by declaring distinct elements to be adjacent if and only if $\langle x,y\rangle…
Groups that have a Partition by Commuting Subsets
Tuval Foguel, Josh Hiller, Mark L. Lewis +1
Let be a nonabelian group. We say that has an abelian partition, if there exists a partition of into commuting subsets of , such that $|A_i|\…
The Solubility Graph Associated With a Finite Group
B. Akbari, Mark L. Lewis, J. Mirzajani +1
Let be a finite group. The solubility graph associated with the finite group , denoted by , is a simple graph whose vertices are the non-trivial elements of $…