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Quotient sets in nonabelian groups

Vsevolod F. Lev

Source record

Source: Crossref

Published: Nov 30, 2025

DOI: 10.1007/s11856-025-2866-3

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Source abstract

Abstract We show that for a finite, nonempty subset A of a group, the quotient set A −1 A ≔ { a 1 −1 a 2 : a 1 , a 2 ∈ A } has size A1A53A\mid A^{-1} A\mid \geq {5\over 3}\mid A \mid ∣ A − 1 A ∣≥ 5 3 ∣ A ∣ , unless A is densely contained in a coset, or in a union of two cosets of a finite subgroup.

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