Abstract
How to extend to non-abelian groups certain combinatorial theorems concerning sums of sets in an abelian group is the subject of this paper. A key result is that the following theorem—free of the hypothesis of normality of the subgroups—holds for the symmetric difference of two sets. Theorem . If X = X + H and Y = Y + K are two finite sets in a group, where H and K are subgroups, and if X + K ≠ X and Y + H ≠ Y, then | X \ Y | + | Y \ X | ⩾ | H | + | K | − 2 | H ∩ K .
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