The Isaacs-Navarro Galois conjecture is proved: for every finite group G and prime l, there is an H0-equivariant bijection between the l'-degree characters of G and those of the normalizer of a Sylow l-subgroup.
The continuity of $p$-rationality of characters and the principal block
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abstract
We study rationality properties of irreducible characters of finite groups. We show that the continuity of $2$-rationality is a phenomenon that can be detected in the principal $2$-block, thus refining a recent result of N. N. Hung. We also propose a conjectural group theoretical criterion for the continuity gap at level $1$ for all primes
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The Isaacs--Navarro Galois conjecture
The Isaacs-Navarro Galois conjecture is proved: for every finite group G and prime l, there is an H0-equivariant bijection between the l'-degree characters of G and those of the normalizer of a Sylow l-subgroup.