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(i) Give example of a group (if exists ) which has a normal subgroup $N\ne\{e\}$ such that

$N \cap Z(G)= \{ e\} $ and $G $ \ $ N$ contains an element of order more than $2$

(ii) Give example of a group (if exists ) such that for every normal subgroup $N\ne\{e\}$ of $G$ ,

$N \cap Z(G)= \{ e\} $ and $G $ \ $ N$ contains an element of order more than $2$

Please Help , thanks in advance .

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    $\begingroup$ Show the work and thought you've put into this already. $\endgroup$ – James Holbert Sep 25 '14 at 14:03
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Let $G=S_3\times S_3$ then $Z(G)=e\times e$ and take $N=A_3\times e$ then you are done.

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  • $\begingroup$ Answer of $i)$. $\endgroup$ – mesel Sep 25 '14 at 14:11

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