1 citations · 1 across the 4 of their papers we have counts for
10 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…
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…