Paper 3, Section I, D

Let $G$ be a group, and suppose the centre of $G$ is trivial. If $p$ divides $|G|$, show that $G$ has a non-trivial conjugacy class whose order is prime to $p$.

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Paper 3, Section I, D

Let $G$ be a group, and suppose the centre of $G$ is trivial. If $p$ divides $|G|$, show that $G$ has a non-trivial conjugacy class whose order is prime to $p$.