Classification of Finite Groups With Equal Left and Right Quotient Sets
Abstract
In this paper, we classify all finite groups G which have the following property: for all subsets A ⊂eq G, we have |AA-1| = |A-1A|. This question is motivated by the problem in additive combinatorics of More Sums Than Difference sets and answers several questions posed in arXiv:2509.00611 [math.NT].
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