What type of study is this?

This is a Quantitative Study study.

October 3, 2025Open Access

Classification of Finite Groups With Equal Left and Right Quotient Sets

HMHaran MouliUniversity of Wisconsin–Madison PSPramana SaldinUniversity of Wisconsin–Madison

Key Points

Finite groups with equal left and right quotient sets exhibit unique properties that facilitate classification.
The study reveals that for any subset of the group, the sizes of left and right quotient sets are identical.
Methods from additive combinatorics are applied to tackle the classification of these finite groups.
Results may have broader implications for understanding patterns in additive combinatorics and related mathematical fields.

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.

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Cite This Study

Mouli et al. (Fri,) studied this question.

synapsesocial.com/papers/68e02f46f0e39f13e7fa2bc3 https://doi.org/https://doi.org/10.48550/arxiv.2509.04717