Abstract
We show that if a finite group G has exactly three rational conjugacy classes, then G also has exactly three rational-valued irreducible complex characters. This generalizes a result of Navarro and Tiep (Trans Amer Math Soc 360:2443–2465, 2008) and partially answers in the affirmative a conjecture of theirs. We also give a family of examples of non-solvable groups with exactly three rational conjugacy classes.
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This work constitutes a portion of the author’s Ph.D. dissertation under the direction of Pham Huu Tiep. Prof. Tiep’s support is gratefully acknowledged. Part of the research was supported by NSF grant DMS-1201374.
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Rossi, D. Finite groups with three rational conjugacy classes. Arch. Math. 110, 99–108 (2018). https://doi.org/10.1007/s00013-017-1127-z
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DOI: https://doi.org/10.1007/s00013-017-1127-z