# H and K are distinct subgroups of a group G with |H| = |K| = 11. Prove that the intersection of H and K is {e}

$H$ and $K$ are subgroups of a group $G$ with $H$ doesn't equal to $K$ and $|H| = |K| = 11$. Prove that $H \cap K = \{e\}$

Can we generalize this post for a prime $p$ so that this shall be a good original for subsequent posts? – user21436 Apr 15 '12 at 16:31
Hint: $H\cap K$ is a subgroup of $H$. What can you say about the subgroups of a group of prime order?