Let G be a finite group, and let S and T be 2 subsets of G such that G does not equal ST. Show that

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- December 26th 2009, 07:43 AMmmsfinite group
Let G be a finite group, and let S and T be 2 subsets of G such that G does not equal ST. Show that

- December 26th 2009, 12:55 PMOpalg
- December 31st 2009, 08:33 AMmms
Could you help me a little bit more? i still can't do this problem >.<

thanks! - December 31st 2009, 08:58 AMOpalg
There are |S| elements in S. There are |T| elements in , and also in its coset . Also, the sets S and are disjoint: for suppose that an element is also in . Then for some . But that implies that , which contradicts the choice of g. Therefore there are |S|+|T| distinct elements in the set , and so .

- December 31st 2009, 10:49 AMmms
ahh i see, thank you!