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arXiv · 1907.04795

Characterizations of nested GVZ-groups by central series

Shawn T. Burkett·Mark L. Lewis
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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.

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Shawn T. Burkett, Mark L. Lewis. 2019-07-10. Characterizations of nested GVZ-groups by central series. https://arxiv.org/abs/1907.04795

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