Navarro–Tiep's conjecture on achieving p-rationality levels at p-elements

Let pp be a prime, let GG be a finite group, and let χ\chi be an irreducible pp'-degree character of GG. The pp-rationality level of a character value is defined using the pp-part of the conductor of that value. Navarro–Tiep's conjecture. If the pp-rationality level of χ\chi is greater than 11, then it is achieved at a pp-element of GG; that is, there exists a pp-element gGg\in G such that

lev(χ(g))=lev(χ)>1.\operatorname{lev}(\chi(g))=\operatorname{lev}(\chi)>1.

The source identifies this with the cited conjecture of Navarro and Tiep and does not state that it has been resolved.

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Sources & referencesView supporting material

Primary source

Nguyen N. Hung, “The continuity of p-rationality and a lower bound for p'-degree characters of finite groups”, arXiv:2205.15899 (2023).

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