Groups where the centers of the irreducible characters form a chain II

TL;DR

This paper provides new characterizations of nested and nested GVZ-groups, including character-free descriptions and characterizations based on normal series, advancing the understanding of their structural properties.

Contribution

It introduces novel characterizations of nested and nested GVZ-groups, especially character-free and normal series-based descriptions, expanding the theoretical framework.

Findings

Characterizations of nested groups and nested GVZ-groups

Character-free descriptions of these groups

Normal series characterizations

Abstract

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 nested GVZ-groups can be defined in terms of the existence of certain normal series.