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A real version of Thompson’s Theorem on Degrees

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Abstract

We extend Thompson’s theorem by taking into account real-valued irreducible characters. In particular, we prove that if G is a finite group generated by its 2-elements and there is an odd prime p dividing the order of the group G, then there is a non-linear real-valued irreducible character of G of degree coprime to p.

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Acknowledgements

The authors would like to thank Gabriel Navarro and Mandi Schaeffer Fry for many useful conversations on this topic. This research is partially supported by the Spanish Ministerio de Ciencia e Innovación PID2019-103854GB-I00 and FEDER funds.

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Authors and Affiliations

  1. Department of Mathematics, University of the Basque Country UPV/EHU, Bilbao, Spain

    Noelia Rizo

  2. Departament de Matemàtiques, Facultat de Matemàtiques, Universitat de València, 46100, Burjassot, Valencia, Spain

    Lucia Sanus

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  1. Noelia Rizo
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  2. Lucia Sanus
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Correspondence to Lucia Sanus.

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Rizo, N., Sanus, L. A real version of Thompson’s Theorem on Degrees. Annali di Matematica 200, 1297–1300 (2021). https://doi.org/10.1007/s10231-020-01038-6

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  • DOI: https://doi.org/10.1007/s10231-020-01038-6

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