The Navarro–Tiep Galois conjecture for \(p=2\)
We prove a recent conjecture of Navarro and Tiep on the 2-rationality of characters of finite groups in relation with the structure of the commutator factor group of a Sylow 2-subgroup. On the way we complete the characterisation of characters of odd degree in quasi-simple groups of Lie type.
KeywordsMcKay conjecture Galois action Rationality Sylow subgroups
Mathematics Subject Classification20C15 20C33
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The Chevie system provided by J. Michel  proved extremely useful for computations on component groups of centralisers of quasi-isolated elements. I like to thank Mandi Schaeffer Fry for her comments on an earlier version.
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