Summary
Letk andm be positive integers. An abelian groupG is said to have ann-cover if there is a subsetS ofG consisting ofn elements such that every non-zero element ofG can be expressed in the formig for some elementg inS and integeri, 1 ≤i ≤ k. Lets n (k) be the largest order of abelian groups that have ann-cover. We investigate the behavior ofs n (k)/k ask → ∞ andn is fixed.
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Dad-del, A.A. Covering abelian groups with cyclic subsets. Aeq. Math. 51, 137–144 (1996). https://doi.org/10.1007/BF01831146
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DOI: https://doi.org/10.1007/BF01831146