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be a finite abelian group with r = 1 or 1 < n1 |... |nr, and let S = (a1,..., at) be a sequence of elements in G. We say S is an unextendible sequence if S is a zero-sum free sequence and for any element g ∈ G, the sequence Sg is not zero-sum free any longer. Let L(G) = ⌈log2 n1 ⌉ +... + ⌈log2 nr ⌉ and d ∗ (G) = ∑r i=1 (ni−1), in this paper we prove, among other results, that the minimal length of an unextendible sequence in G is not bigger than L(G), and for any integer k, where L(G) ≤ k ≤ d ∗ (G), there exists at least one unextendible sequence of length k.

Year: 2010

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