The Erdős–Heilbronn problem for finite groups

Abstract

Additive Number Theory can be best described as the study of sums of sets of integers. A simple example is given two subsets A and B of a set of integers, what facts can we determine about A + B where A + B := {a + b | a ∈ A and b ∈ B}? We will state a result regarding this example shortly. We note that a very familiar problem in Number Theory, namely Lagrange’s theorem that every nonnegative integer can be written as the sum of four squares, can be expressed in terms of sumsets. In particular, if we let N0 be the set of nonnegative integers and if we let S be the set of all integers that are perfect squares, then Lagrange’s Theorem has the form