This time I'm having trouble with the following exercise:
Being $|G| = 20$ and $H$ and $K$ subgroups of $G$ whose order is 5, prove that $K = H$.
I'm also recommended to start by proving that $|H \cap K| = 5$.
My draft:
Let $x \in (H \cap K)\setminus{\{e\}}$. Then $|x|$ divides $|H| = |K| = 5$. Because $x \neq e$, $|x|$ can only be 5. So $|
= H \cap K| = 5$ .
Is this part OK?
But now, on to prove that $H = K$, I've been wandering around unsuccessfully (my rubber is already half the size it was earlier today :p). Can you drop any hint on this matter?
Thanks for taking the time to read!