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A Note on the Rational Non-linear Characters of Groups

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Abstract

We study finite groups with rational valued non-linear characters and obtain the structure of these types of groups with derived subgroup of prime order. In particular, in the case of the size of derived subgroup of a group is two we conclude that this group is rational if and only if the group is a direct product of an extraspecial 2-group with an elementary abelian 2-group.

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Acknowledgments

The authors express their deep gratitude to the referee for her/his extensive comments leading to a much clearer presentation.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Shahed University, Tehran, Iran

    M. Norooz-Abadian & H. Sharifi

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  1. M. Norooz-Abadian
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  2. H. Sharifi
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Correspondence to H. Sharifi.

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Presented by: Alistair Savage

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Norooz-Abadian, M., Sharifi, H. A Note on the Rational Non-linear Characters of Groups. Algebr Represent Theor 23, 1977–1982 (2020). https://doi.org/10.1007/s10468-019-09920-5

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  • DOI: https://doi.org/10.1007/s10468-019-09920-5

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