ar X iv : 0 80 1 . 37 92 v 1 [ m at h . N T ] 2 4 Ja n 20 08 INVERSE ZERO - SUM PROBLEMS III
نویسندگان
چکیده
{g1, g2} is a generating set of G with ord(g2) = n2, x1, . . . , xn2+(1−s)n1 ∈ [0, n1 − 1], x1 + . . . + xn2+(1−s)n1 = n1 − 1, s ∈ [1, n2/n1], and either s = 1 or n1g1 = n2g2. Thus Property B is multiplicative, and if G = Cn1 ⊕Cn2 with 1 < n1 |n2 is a group of rank two, and for every prime divisor p of n1 the group Cp ⊕Cp has Property B, then the minimal zero-sum sequences of maximal length over G are explicitly characterized. In Section 2, we fix our notation and gather the necessary tools (apart from former work on Property B and classical addition theorems, we use a confirmed conjecture of Y. ould Hamidoune, see Theorem 2.7). Section 3 contains some straightforward lemmas. The proof of the Theorem consists of two major parts: the first is given in Section 4 and the second, more involved one, is given in Section 5. The Corollary is mainly based on the Theorem above, on former work of the authors [5], and on recent work by Wolfgang A. Schmid [13]. Its proof only needs a few lines and is given in Section 6.
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تاریخ انتشار 2008