Difference bases in finite Abelian groups

Abstract

A subset B of a group G is called a difference basis of G if each element g ∈ G can be written as the difference g = ab −1 of some elements a, b ∈ B. The smallest cardinality |B| of a difference basis B ⊂ G is called the difference size of G and is denoted by ∆[G]. The fraction ð[G] := ∆[G]

Bases in finite groups of small order

“…Difference bases and difference characteristics in dihedral and Abelian groups were investigated in [3,4]. Difference bases have applications in the study of structure of superextensions of groups, see [1,5,9].…”

“…In fact, this problem has been studied in the literature. In particular, G. Kozma and A. Lev [19] proved that each finite group G has basis characteristic δ[G] ≤ 4 A standard model of a cyclic group of order n is the multiplicative group C n = {z ∈ C : z n = 1} of n-th roots of 1. The group C n is isomorphic to the additive group of the ring Z n = Z/nZ.…”