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Math Help - proving an inequality

  1. #1
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    proving an inequality

    Let G be a non-abelian finite group, Z(G) be the center of G and C_{G}(x) be the centralizer of the element x in G. Let x \in G \setminus Z(G), so we have |G| \geq 2|C_{G}(x)|. Now how can I prove that |G \setminus C_{G}(x)|>(|G|-|Z(G)|)/2 ?
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  2. #2
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    Re: 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.

    proving an inequality-mhfgroupinequality.png
    Thanks from xixi
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