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Found problems: 1

2011 Gheorghe Vranceanu, 1
Tags: abstract algebra , group theory , fucntions
[b]a)[/b] Let $ B,A $ be two subsets of a finite group $ G $ such that $ |A|+|B|>|G| . $ Show that $ G=AB. $ [b]b)[/b] Show that the cyclic group of order $ n+1 $ is the product of the sets $ \{ 0,1,2,\ldots ,m \} $ and $ \{ m,m+1,m+2,\ldots ,n\} , $ where $ 0,1,2,\ldots n $ are residues modulo $ n+1 $ and $ m\le n. $