Finite groups with three rational conjugacy classes |
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Authors: | Dan Rossi |
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Institution: | 1.Department of Mathematics,University of Arizona,Tucson,USA |
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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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