English

GVZ-groups, Flat Groups, and CM-Groups

Group Theory 2020-09-30 v2

Abstract

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 characters. We also show that certain CM-groups can be characterized as GVZ-groups whose irreducible character values lie in the prime field.

Keywords

Cite

@article{arxiv.1909.05841,
  title  = {GVZ-groups, Flat Groups, and CM-Groups},
  author = {Shawn T. Burkett and Mark L. Lewis},
  journal= {arXiv preprint arXiv:1909.05841},
  year   = {2020}
}

Comments

8 pages - Based on referee's report for the previous paper "GVZ-groups", that was substantially revised and subsumed by this paper

R2 v1 2026-06-23T11:13:49.574Z