Characterizations of nested GVZ-groups by central series
Group Theory
2019-07-11 v1 Representation Theory
Abstract
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 nilpotent groups are the so-called nested GVZ-groups --- groups where the centers of the irreducible characters form a chain, and where every irreducible character vanishes off of its center. In this paper, we show that nested GVZ-groups can be characterized by the existence of a certain ascending central series, or by the existence of a certain descending central series.
Cite
@article{arxiv.1907.04795,
title = {Characterizations of nested GVZ-groups by central series},
author = {Shawn T. Burkett and Mark L. Lewis},
journal= {arXiv preprint arXiv:1907.04795},
year = {2019}
}