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Let $G$ be a finitely generated group with generators $X=\{g_1,g_2,\dots,g_m\}$ and $n$ be a positive integer such that the $n$-th power of every element in $X$ is the identity.

Is it true that $\mathrm{exp}(G) | n$? Clearly for abelian groups it is true. I think that it can develop to other specific groups.

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    No - there exist finitely generated torsion groups with unbounded exponent.2012-10-30
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    user1729 in this question G is not torison group and only generators have finite order.2012-10-30
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    Then you should say so in your question! So, can I ask you what you have tried? Surely this is not difficult - this is just the definition of exponent!2012-10-30
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    Just curious why you "undid" the edits that were made to improve formatting (using LaTeX)? The added "if No" is fine, but you deliberately "undid" exactly what was done to format your question.2012-10-30
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    @mojtabafarazi: Since you are new here, so welcome; so you'd better register here and fix your accepted rate. Welcome mojtaba. :-)2012-10-31
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    @mojtabafarazi I corrected your copious English grammar and spelling mistakes as well as adding missing Latex. If you undo the changes bad things will happen.2012-11-21

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