Classification of Finite Groups With Equal Left and Right Quotient Sets

2025/09/05 by Mouli, Haran, Saldin, Pramana
#11P70 (Secondary) #20E34 (Primary) #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2509.04717

Abstract

In this paper, we classify all finite groups G which have the following property: for all subsets A ⊆ 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].

Cited by

• Comparing Left and Right Quotient Sets in Groups

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