%0 Journal Article %A PalacĂ­n Cruz, Daniel %T Finite groups contain large centralizers %D 2021 %@ 0021-2172 %@ 1565-8511 %U https://hdl.handle.net/20.500.14352/98559 %X Every finite non-abelian group of order n has a non-central element whose centralizer has order exceeding n^{1/3}. The proof does not rely on the classification of finite simple groups, yet it uses the Feit-Thompson theorem. %~