# 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 $H \cap K = \{e\}$

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Hint: Lagrange's Theorem. –  user21436 Apr 15 '12 at 16:19
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
@KannappanSampath: That seems like a good idea. Would it be considered impolite for you to just go ahead and change it? –  Tara B Apr 16 '12 at 7:57
@TaraB It would be impolite. May be, I would make a meta post in the near future. Thank you for dropping by to tell me what you feel. I'd ping you when I write a question at the meta. Regards, –  user21436 Apr 16 '12 at 10:57
Hint: $H\cap K$ is a subgroup of $H$. What can you say about the subgroups of a group of prime order?