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Finite groups have local non-Schur centralizers. (English) Zbl 0820.20025
Using the classification of the finite simple groups the authors prove the following theorem: If $$G$$ is a finite group of order divisible by the prime $$p$$ then $$G$$ contains a $$p$$-singular element $$g$$ whose $$p$$-part is not contained in the commutator subgroup of $$C_ G(g)$$.

##### MSC:
 20D20 Sylow subgroups, Sylow properties, $$\pi$$-groups, $$\pi$$-structure 20D25 Special subgroups (Frattini, Fitting, etc.)
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##### References:
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