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.
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Shawn T. Burkett 1; Mark L. Lewis 1
CC-BY 4.0
@article{CRMATH_2021__359_3_355_0,
author = {Shawn T. Burkett and Mark L. Lewis},
title = {GVZ-groups, {Flat} groups, and {CM-Groups}},
journal = {Comptes Rendus. Math\'ematique},
pages = {355--361},
publisher = {Acad\'emie des sciences, Paris},
volume = {359},
number = {3},
year = {2021},
doi = {10.5802/crmath.185},
language = {en},
}
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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