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Questions on group theory which concern finite groups.

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Prime divisor of finite group

We know that the number of elements of order $k$ in a finite group $G$ is equal to $\sum |cl_{G}(x_{i})|$=$\sum|G/C_{G}(x_{i})|$ such that $|x_{i}|=k$. It is clear that for a prime $p$ if $p\mid |cl_{ …