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    Finite groups with three rational conjugacy classes

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    Rossi-3_Rationals_Short.pdf
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    Final Accepted Manuscript
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    Author
    Rossi, Dan
    Affiliation
    Univ Arizona, Dept Math
    Issue Date
    2018-02
    Keywords
    Rational irreducible character
    Rational conjugacy class
    
    Metadata
    Show full item record
    Publisher
    SPRINGER BASEL AG
    Citation
    Rossi, D. Arch. Math. (2018) 110: 99. https://doi.org/10.1007/s00013-017-1127-z
    Journal
    ARCHIV DER MATHEMATIK
    Rights
    © Springer International Publishing AG, part of Springer Nature 2017
    Collection Information
    This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.
    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.
    Note
    12 month embargo; published online: 07 December 2017
    ISSN
    0003-889X
    1420-8938
    DOI
    10.1007/s00013-017-1127-z
    Version
    Final accepted manuscript
    Sponsors
    NSF [DMS-1201374]
    Additional Links
    http://link.springer.com/10.1007/s00013-017-1127-z
    ae974a485f413a2113503eed53cd6c53
    10.1007/s00013-017-1127-z
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