Show that a group can not be expressed as union of two of its proper subgroups

Question

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

You might want to check also this entry – Nicky Hekster Sep 04 '13 at 20:45 — Nicky Hekster, Sep 04 '13 at 20:45

score 17 · Answer 1 · answered Sep 04 '13 at 19:59

17

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

answered Sep 04 '13 at 19:59

Brian M. Scott

I was just about to ask how to continue and I got it :) (+1) – Belgi Sep 04 '13 at 20:01

1 Answers1