38 citations · 154 across the 58 of their papers we have counts for
7 papers · 2 filters
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…
Toward a Classification of the Supercharacter Theories of
Shawn T. Burkett, Mark L. Lewis
In this paper, we study the superscharacter theories of elementary abelian -groups of order . We show that the supercharacter theories that arise from the direct product co…
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…
On solvable groups with one vanishing class size
Mariagrazia Bianchi, Rachel D. Camina, Mark L. Lewis +1
Let be a finite group, and let cs be the set of conjugacy class sizes of . Recalling that an element of is called a \emph{vanishing element} if there exists an…
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|\…
A Frobenius group analog for Camina triples
Shawn T. Burkett, Mark L. Lewis
Frobenius groups are an object of fundamental importance in finite group theory. As such, several generalizations of these groups have been considered. Some examples include: A Fro…