Abstract
Every finite non-abelian group of order n has a non-central element whose centralizer has order exceeding n1/3. The proof does not rely on the classification of finite simple groups, yet it uses the Feit-Thompson theorem.
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Research supported by MTM2017-86777-P as well as by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) — Project number 2100310301, part of the ANR-DFG program GeoMod.
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Palacín, D. Finite groups contain large centralizers. Isr. J. Math. 244, 621–624 (2021). https://doi.org/10.1007/s11856-021-2183-4
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DOI: https://doi.org/10.1007/s11856-021-2183-4