Vol. 122, No. 1, 1986

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Abelian groups and packing by semicrosses

Dean Robert Hickerson and Sherman K. Stein

Vol. 122 (1986), No. 1, 95–109
Abstract

Motivated by a question about geometric packings in n-dimensional Euclidean space, Rn, 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, a1,a2,,an, such that the kn elements iaj, 1 i k, are distinct and not 0. We will show that for n fixed, g(k,n) 2cos(π∕n)k32.

Mathematical Subject Classification 2000
Primary: 52A45, 52A45
Secondary: 20K01
Milestones
Received: 14 June 1984
Published: 1 March 1986
Authors
Dean Robert Hickerson
Sherman K. Stein