1 citations · 1 across the 5 of their papers we have counts for
13 papers
Partial GVZ-groups
Shawn T. Burkett, Mark L. Lewis
Following the literature, a group is called a group of central type if has an irreducible character that vanishes on . Motivated by this definition, we say…
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.
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…
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…
Supercharacter theory via the group determinant
Shawn T. Burkett
Ferdinand Georg Frobenius is generally considered the creator of character theory of finite groups. This achievement came from the study of the group determinant, which is the dete…
A characterization of Nested Groups in terms of conjugacy classes
Shawn T. Burkett, Mark L. Lewis
A group is nested if the centers of the irreducible characters form a chain. In this paper, we will show that there is a set of subgroups associated with the conjugacy classes of g…
GVZ-groups, Flat Groups, and CM-Groups
Shawn T. Burkett, Mark L. Lewis
We show that a group is a GVZ-group if and only if it is a flat group. We show that the nilpotence class of a GVZ-group is bounded by the number of distinct degrees of irreducible…
Characterizations of nested GVZ-groups by central series
Shawn T. Burkett, Mark L. Lewis
Many properties of groups can be defined by the existence of a particular normal series. The classic examples being solvability, supersolvability and nilpotence. Among the nilpoten…
Vanishing-off subgroups and supercharacter theory products
Shawn T. Burkett, Mark L. Lewis
In this paper, we study the vanishing-off subgroups of supercharacters, and use these to determine several new characterizations of supercharacter theory products. In particular, w…
A Jördan-Holder type theorem for supercharacter theories
Shawn T. Burkett
The Jordan-Hölder Theorem is a general term given to a collection of theorems about maximal chains in suitably nice lattices. For example, the well-known Jordan-Hölder type theorem…
An analog of nilpotence arising from supercharacter theory
Shawn T. Burkett
The goal of this paper is to generalize several group theoretic concepts such as the center and commutator subgroup, central series, and ultimately nilpotence to a supercharacter t…
Positive Self-Dual Hopf Algebras of Galois Characters
Farid Aliniaeifard, Shawn Burkett
By using the action of certain Galois groups on complex irreducible characters and conjugacy classes, we define the Galois characters and Galois classes. We will introduce a set of…
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…