Let G be a non-abelian finite group, Z(G) be the center of G and be the centralizer of the element x in G. Let , so we have . Now how can I prove that ?

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- Mar 4th 2013, 07:07 PMxixiproving an inequality
Let G be a non-abelian finite group, Z(G) be the center of G and be the centralizer of the element x in G. Let , so we have . Now how can I prove that ?

- Mar 7th 2013, 08:02 PMjohngRe: proving an inequality
I assume that \ means set minus. Your problem really has nothing to do with centralizers and the center. Here's a solution.

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