38 citations · 154 across the 58 of their papers we have counts for
6 papers · 2 filters
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…
Groups where the centers of the irreducible characters form a chain II
Shawn T. Burkett, Mark L. Lewis
In this paper, we determine new characterizations of nested and nested GVZ-groups, including character-free characterizations, but we additionally show that nested groups and neste…
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…
Groups where the centers of the irreducible characters form a chain
Mark L. Lewis
We consider groups where the centers of the irreducible characters form a chain. We obtain two alternate characterizations of these groups, and we obtain some information regarding…
-groups with exactly four codegrees
Sarah Croome, Mark L. Lewis
Let be a -group and let be an irreducible character of . The codegree of is given by . Du and Lewis have shown that a -group with exact…