Abelian groups and packing by semicrosses

Abstract

Motivated by a question about geometric packings in ^-dimensional Euclidean space, R", we consider the following problem about finite abelian groups. Let n be an integer, n > 3, and let k be a positive integer. Let g(k,n) be the order of the smallest abelian group in which there exist n elements, a l9 a 2 ,...,a n , such that the kn elements ia p 1 < i < k, are distinct and not 0. We will show that for n fixed, g(k,n)~ 2cos(/n)k 3/2 .