38 citations · 154 across the 58 of their papers we have counts for
6 papers · 2 filters
Centralizers of Camina -groups of nilpotence class
Mark L. Lewis
Let be a Camina -group of nilpotence class . We prove that if , then . We also prove that if has only one or two abelian…
Variations on average character degrees and -nilpotence
Mark L. Lewis
We prove that if is an odd prime, is a solvable group, and the average value of the irreducible characters of whose degrees are not divisible by is strictly less th…
Landau's theorem, fields of values for characters, and solvable groups
Mark L. Lewis
When is solvable group, we prove that the number of conjugacy classes of elements of prime power order is less than or equal to the number of irreducible characters with values…
Fitting heights of solvable groups with no nontrivial prime power character degrees
Mark L. Lewis
We construct solvable groups where the only degree of an irreducible character that is a prime power is and that have arbitrarily large Fitting heights. We will show that we ca…
Groups with exactly two supercharacter theories
Shawn Burkett, Jonathan Lamar, Mark L. Lewis +1
In this paper, we classify those finite groups with exactly two supercharacter theories. We show that the solvable groups with two supercharacter theories are and $S…
The character degree ratio and composition factors of a finite group
Mark L. Lewis, Hung Ngoc Nguyen
For a finite non-abelian group let $\rat(G)$ denote the largest ratio of degrees of two nonlinear irreducible characters of . We prove that the number of non-abelian composi…