Pleaseeee Helppp! I dont solve it

• July 31st 2008, 05:21 AM
mathemanyak
Pleaseeee Helppp! I dont solve it
Let G be a group and Let A,B<=G
|A|+|B|>G
Show that G=AB
• July 31st 2008, 06:39 AM
NonCommAlg
Quote:

Originally Posted by mathemanyak
Let G be a group and Let A,B<=G
|A|+|B|>G
Show that G=AB

we only need to prove that $\forall g \in G: \ A \cap gB \neq \emptyset.$ so suppose, on the contrary, that $\exists g \in G: \ A \cap gB = \emptyset.$

then: $|G| \geq |A \cup gB|=|A|+|gB|=|A|+|B| > |G|,$ which is impossible! Q.E.D.
• August 4th 2008, 03:11 AM
mathemanyak
but
but A and B subgorup