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is the center of a finitely generated fc group (a group in which every conjugacy class is finite) also finitely generated? And if yes, how can I prove it?

Thanks in advance

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    All centralizers have finite index, so the intersection of the centralizers of a finite generating set, which is equal to the center, also has finite index and hence is finitely generated.2012-07-05
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    For a proof that subgroups of finite index in a finitely generated group are finitely generated, see [here](http://math.stackexchange.com/q/13062/742).2012-07-05
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    Thank you both very much, i got it now!2012-07-05

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