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Group Elements Whose Character Values are Roots of Unity

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Abstract

We classify all finite groups G that possess an element x ∈ G such that every irreducible character of G takes a root of unity value at x.

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Acknowledgements

The authors would like to thank the referees for their careful reading of the manuscript. The comments and suggestions are very helpful and have improved our presentation. Part of this work was done while the third author was visiting the Vietnam Institute for Advanced Study in Mathematics (VIASM), and he thanks the VIASM for financial support and hospitality.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Kent State University, Kent, OH, 44242, USA

    Mark L. Lewis

  2. Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Leibniz Universität Hannover, 30167, Hannover, Germany

    Lucia Morotti

  3. Department of Mathematics and Statistics, Binghamton University, Binghamton, NY, 13902-6000, USA

    Hung P. Tong-Viet

Authors
  1. Mark L. Lewis
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  2. Lucia Morotti
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  3. Hung P. Tong-Viet
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Correspondence to Hung P. Tong-Viet.

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Dedicated to Pham Huu Tiep on his 60th birthday.

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Lewis, M.L., Morotti, L. & Tong-Viet, H.P. Group Elements Whose Character Values are Roots of Unity. Vietnam J. Math. 52, 379–388 (2024). https://doi.org/10.1007/s10013-023-00611-9

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  • DOI: https://doi.org/10.1007/s10013-023-00611-9

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Mathematics Subject Classification (2010)

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