Covering abelian groups with cyclic subsets
ALl Akbar · 2005
Let k and m be positive integers. An abelian group G is said to have an n-cover if there is a subset S of G consisting of n elements such that every non-zero element of G can be expressed in the form ig for some element g in S and integer i, 1 _< i <_ k. Let s,,(k) be the largest order of abelian groups that have an n-cover. We investigate the behavior of s,(k)/k as k --* oo and n is fixed.