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Why is it that any two distinct subgroups of G of order p (prime) intersect in 1?

It says so here on page 29.

But why is it?

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    @lhf: Done. $\quad$2012-05-06

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Converting my comment to an answer to get the question off the Unanswered list:

HINT: If $H$ and $K$ are subgroups of $G$, $H\cap K$ is a subgroup of $H$ and of $K$. What are the only subgroups of a group of prime order?