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Let $N$ be a normal subgroup of group $G$. There exists a prime $p$ such that $G/O^p(N)$ is simple group. Is there any element in the center of group $G$?

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    May I ask what is $O^p(N)$. I don't know this notation. Thanks.2012-10-19
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    @BabakSorouh: $O^p(N)$ is the smallest normal subgroup of $p$-power index. I explain a few of its properties and put it in context in my answer.2012-10-19
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    @JackSchmidt: Thanks Jack, noting me that. You did below as usual the best(+1).2012-10-20

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