GVZ-groups, Flat groups, and CM-Groups

Burkett, Shawn T.; Lewis, Mark L.

Comptes Rendus. Mathématique, Tome 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.

Classification : 20C15

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