Quotient sets in nonabelian groups

2024/04/10 by Lev, Vsevolod F.
#11B13 #11P70 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2404.06887

Abstract

We show that for a finite, nonempty subset A of a group, the quotient set A^-1A:=\a₁^-1a₂\colon a₁,a₂∈ A\ has size |A^-1A|≥\frac53 |A|, unless A is densely contained in a coset, or in a union of two cosets of a finite subgroup.

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