A note on sumsets of subgroups in \mathbb Z_p^*

2013/03/12 by Derrick Hart, Hart, Derrick · 1 citation
Computer Science · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1303.2729

openalex publication_date 2013/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a multiplicative subgroup of \mathbb Z_p^*. Define the k-fold sumset of A to be kA=\x₁+…+x_k:x_i ∈ A,1≤ i≤ k\. We show that 6A⊇ \mathbb Z_p^* for |A| > p^\frac 1123 +ε. In addition, we extend a result of Shkredov to show that |2A|≫ |A|^{\frac 85-ε} for |A|≪ p^{\frac 59}.

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