On Minkowski product size: The Vosper's property
Abstract
A subset S of a group G is said to be a Vosper's subset if |A AS| (|G|-1,|A|+|S|), for any subset A of G with |A| 2. In the present work, we describe Vosper's subsets. Assuming that S is not a progression and that |S-1 S|, |S S-1| <2 |S|,|G'|-1, we show that there exist an element a∈ S, and a non-null subgroup H of G' such that either S-1HS =S-1S a-1Ha or SHS-1 =SS-1 aHa-1, where G' is the subgroup generated by S-1S.
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