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This is a Quantitative Study study.

October 3, 2025Open Access

Classification of Finite Groups With Equal Left and Right Quotient Sets

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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.

Implication

This paper classifies finite groups demonstrating equal quotient set sizes, implying significant links to additive combinatorics.

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. (2025) studied this question.

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

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Implication

This paper classifies finite groups demonstrating equal quotient set sizes, implying significant links to additive combinatorics.

Classification of Finite Groups With Equal Left and Right Quotient Sets

Key Points

Implication

Abstract

Discussion

Cite This Study

Classification of Finite Groups With Equal Left and Right Quotient Sets

Key Points

Implication

Abstract

Discussion

Cite This Study

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