Let G be a finite abelian group. A nonempty subset A in G is called a basis of order hif hA = G; when hA ̸= G, it is called a nonbasis of order h. Our interest is in all possiblesizes of hA when A is a nonbasis of order h in G of maximum size; we provide the completeanswer when h = 2 or h = 3.
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