Group Elements Whose Character Values are Roots of Unity

Mark L. Lewis1, Lucia Morotti2, Hung P. Tong-Viet3
1Department of Mathematical Sciences, Kent State University, Kent, USA
2Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Leibniz Universität Hannover, Hannover, Germany
3Department of Mathematics and Statistics, Binghamton University, Binghamton, USA

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Berkovich, Y.G., Kazarin, L.S., Zhmud’, E.M.: Characters of Finite Groups, vol. 2, 2nd edn. De Gruyter Expositions in Mathematics, vol. 64. De Gruyter, Berlin (2019)

The GAP Group, GAP – Groups, algorithms, and programming, Version 4.10.1 (2019). https://www.gap-system.org

Granville, A., Ono, K.: Defect zero p-blocks for finite simple groups. Trans. Amer. Math. Soc. 348, 331–347 (1996)

Isaacs, I.M.: Character Theory of Finite Groups. Corrected reprint of the 1976 original. AMS Chelsea Publishing, Providence, RI (2006)

Isaacs, I.M., Navarro, G., Wolf, T.R.: Finite group elements where no irreducible character vanishes. J. Algebra 222, 413–423 (1999)

Isaacs, I.M., Keller, T.M., Meierfrankenfeld, U., Moretó, A.: Fixed point spaces, primitive character degrees and conjugacy class sizes. Proc. Amer. Math. Soc. 134, 3123–3130 (2006)

Moretó, A., Tiep, P.H.: Nonsolvable groups have a large proportion of vanishing elements. Isr. J Math. https://doi.org/10.1007/s11856-022-2395-2 (2022)

Moretó, A., Wolf, T.R.: Orbit sizes, character degrees and Sylow subgroups. Adv. Math. 184, 18–36 (2004)

Morotti, L.: Sign conjugacy classes of the alternating groups. Commun. Algebra 46, 1066–1079 (2018)

Taunt, D.R.: On A-groups. Math. Proc. Camb. Philos. Soc. 45, 24–42 (1949)