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Show that a group can not be expressed as union of two of its proper subgroups. I am not sure how to start.

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HINT: Suppose that $H,K<G$, and let $h\in H\setminus K$ and $k\in K\setminus H$; where is $hk$?

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  • $\begingroup$ I was just about to ask how to continue and I got it :) (+1) $\endgroup$
    – Belgi
    Sep 4, 2013 at 20:01

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