If A and B are mere SUBSETS of G and |A| + |B| > |G|, then AB = G.(adsbygoogle = window.adsbygoogle || []).push({});

My thought is that a "weakest case" would be where A has |G|/2 + 1 elements (if |A| + |B| > |G|, then one of A or B must have over half of G's elements) and |G|/2 of them form a subgroup of G. Then taking B= the subgroup, it is true that AB = G because that one stray element when multiplied with the subgroup gives the rest of G. So, since AB = G in this case, it must be true in general.

Is this valid, or should I be doing something else?

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# Group generated by two sets

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