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The restricted sumsets in finite abelian groups

Shanshan Du, Hao Pan

Abstract

Suppose that $k\geq 2$ and $A$ is a non-empty subset of a finite abelian group $G$ with $|G|>1$. Then the cardinality of the restricted sumset $$ k^\wedge A:=\{a_1+\cdots+a_k:\,a_1,\ldots,a_k\in A,\ a_i\neq a_j\text{ for }i\neq j\} $$ is at least $$ \min\{p(G), k|A|-k^2+1\}, $$ where $p(G)$ denotes the least prime divisor of $|G|$.

The restricted sumsets in finite abelian groups

Abstract

Suppose that and is a non-empty subset of a finite abelian group with . Then the cardinality of the restricted sumset is at least where denotes the least prime divisor of .
Paper Structure (2 sections, 1 theorem, 62 equations)

This paper contains 2 sections, 1 theorem, 62 equations.

Table of Contents

  1. Introduction
  2. The proof of Theorem \ref{['mainT']}

Key Result

Theorem 1.1

Suppose that $G$ is a finite abelian group with $|G|>1$. For any $\emptyset\neq A\subseteq G$,

Theorems & Definitions (1)

  • Theorem 1.1