Any small multiplicative sugroup is not a sumset

2017/02/03 by Ilya D. Shkredov, Shkredov, Ilya D.
Mathematics · #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1702.01197

openalex publication_date 2017/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that for an arbitrary ε>0 and any multiplicative subgroup Γ⊆ F_p, 1≪ |Γ| ≤ p^{2/3 -ε} there are no sets B, C ⊆ F_p with |B|, |C|>1 such that Γ=B+C. Also, we obtain that for 1≪ |Γ| ≤ p^6/7-ε and any ξ≠ 0 there is no a set B such that ξΓ+1=B/B.

Citations

• Quadratic residues and difference sets

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