Explicit calculations and asymptotic behaviour of a distance measure between finite Abelian groups (Q1603242)

The author investigates properties of a distance function on a set of finite Abelian groups of equal order. This metric was introduced by \textit{R. Wolf} [Acta Math. Hung. 78, No. 1-2, 25-37 (1998; Zbl 0902.11030)]. The version considered in this paper is redefined to limit the number of possible bijections between the groups to so called ``natural'' bijections. This allows the author to provide closed-form formulae for the distance between a cyclic group of an odd order and some other finite Abelian groups. The asymptotic behavior of the distance function is also studied.