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Suppose that $G$ is finite group with two normal subgroups $N$ and $K$ such that $K. Is true that the center of $G/K$ is subset of the center of $G/N$?

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    $G/K$ is not necessarily a *subset* of $G/N$, so what do you mean precisely? If $Z(G/K)=L/K$ and $Z(G/N)=M/N$, do you want to know if $L \subset M$?2012-10-23
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    If $hK\in Z(G/K)$ then are you wanting to prove that $hK\in Z(G/K)$? Well, if $hK\in Z(G/K)$ then $[g, h]\in K\leq N$ for all $g\in G$. So, we're done.2012-10-23
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    @user1729 I think you mean "wanting to prove that $hN \in Z(G/N)$" right?2012-10-23
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    @NickyHekster Yup, thanks.2012-10-23
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    Thanks for all comments. Yes Nicky I want to know if $L$ is subset of $M$?2012-10-23
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    @Morad: This is what I essentially prove in my comment. I say essentially, because (assuming $L$ and $M$ are fixed transversals) $L$ might be $a, b, \ldots$ but then $M$ might have $an$ in place of $a$, where $n\in N$. However, $a$ and $an$ are equal mod $N$.2012-10-23

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