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Comptes Rendus. Mathématique
Algebra, Group Theory
GVZ-groups, Flat groups, and CM-Groups
Comptes Rendus. Mathématique, Volume 359 (2021) no. 3, pp. 355-361.

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.

Received:
Revised:
Accepted:
Published online:
DOI: https://doi.org/10.5802/crmath.185
Classification: 20C15
Shawn T. Burkett 1; Mark L. Lewis 1

1. Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242, U.S.A.
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Shawn T. Burkett; Mark L. Lewis. GVZ-groups, Flat groups, and CM-Groups. Comptes Rendus. Mathématique, Volume 359 (2021) no. 3, pp. 355-361. doi : 10.5802/crmath.185. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.185/

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