On the largest Brauer and p′-character degrees Article Swipe

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Alexander Moretó ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.1016/j.jalgebra.2023.04.021 · OA: W4367311338

Let K be a field of characteristic p>0. We prove that if all irreducible representations over K of a finite group G have degree at most n, then G has a characteristic subgroup N of index bounded above in terms of n such that its derived subgroup N′ is a p-group. Our proof of this result relies on the celebrated Larsen-Pink theorem. We also show that every finite group G has a solvable p-nilpotent subgroup of index bounded above in terms of the largest p′-degree of the complex irreducible characters of G.