Abstract
A finite group whose all irreducible characters are rational valued is called a rational group. Using the concept of transversal action, we get a sufficient condition on non Abelian rational groups that guarantees every Sylow 2-subgroup is also rational. This gives a partial answer to an old conjecture rationality of Sylow 2-subgroup of rational group.
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References
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Norooz-Abadian, M., Sharifi, H. A note on the rationality of Sylow 2-subgroups of rational groups. Math Notes 101, 1066–1067 (2017). https://doi.org/10.1134/S0001434617050352
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DOI: https://doi.org/10.1134/S0001434617050352