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Let $G$ be a finite group and $N\lhd G$. For every $x\in G-N$ we have $$C_G(x)N/N\leq C_{G/N}(Nx)$$ where $C_G(x)$ is the centralizer of $x$ in $G$. But I don't know what is the qutient.

In fact I want to know the $[C_{G/N}(Nx):C_G(x)N/N]$. It is more important when $N=Z(G)$.

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Writing quotient groups as straight fractions can look somehow confusing. I think it's better with a slash. – DonAntonio Dec 23 '12 at 10:05
Well the answer depends on $G$, $N$ and $x$. It is not clear what kind of answer your are looking for! – Derek Holt Dec 23 '12 at 11:16

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