Let G be a group and Let A,B<=G

|A|+|B|>G

Show that G=AB

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- Jul 31st 2008, 04:21 AMmathemanyakPleaseeee Helppp! I dont solve it
Let G be a group and Let A,B<=G

|A|+|B|>G

Show that G=AB - Jul 31st 2008, 05:39 AMNonCommAlg
we only need to prove that $\displaystyle \forall g \in G: \ A \cap gB \neq \emptyset.$ so suppose, on the contrary, that $\displaystyle \exists g \in G: \ A \cap gB = \emptyset.$

then: $\displaystyle |G| \geq |A \cup gB|=|A|+|gB|=|A|+|B| > |G|,$ which is impossible! Q.E.D. - Aug 4th 2008, 02:11 AMmathemanyakbut
but A and B subgorup