CERTAIN COVERINGS OF FINITE HOMOCYCLIC ABELIAN GROUPS

Abstract

Let G be a finite Abelian group written additively which is the n-fold direct sum of cyclic groups of order k. Denote A the union of these direct summands of G. Let r(k, n) be the minimum of the cardinality of subsets B <;;; G for which G = A + B holds. The inequality r(tk, n) :s;: tn-lr(k, n) is proved in this note.