張海燕+劉庚

摘 要：如果在群CnCn中，每個(gè)含有2n-1個(gè)元素的極小零和序列中都包含一些階數(shù)為n-1的元素，那么我們稱正整數(shù)n具有性質(zhì)B。在二維阿貝爾群的零和理論中，性質(zhì)B是一個(gè)中心議題。關(guān)于性質(zhì)B這一問(wèn)題最早是由高維東教授和A.Geroldinger提出并進(jìn)行研究[1-3]。之后，他們證明了如果n具有性質(zhì)B[4-6]，當(dāng)n大于等于6時(shí)，2n也具有性質(zhì)；還證明了如果n∈{2，3，4，5，6，7}，n具有性質(zhì)B。在文[7]中，我們證明了n=10時(shí)，n具有性質(zhì)B。本文證明n=8時(shí)，n也具有性質(zhì)B。

關(guān)鍵詞：阿貝爾群；零和子列；性質(zhì)B

DOI：10.15938/j.jhust.2017.06.021

中圖分類號(hào)： O156.1

文獻(xiàn)標(biāo)志碼： A

文章編號(hào)： 1007-2683（2017）06-0113-03

Abstract：We say a positive integer n has Property B if every minimal zerosum subsequence of 2n-1 elements in CnCn contains some elements n-1 times. Property B is a central topic in zerosum theory on abelian group G with rank two. Property B has been first formulated and investigated by professer W.D.Gao and A.Geroldinger in [1-3]. It has been proved that if n≥6 and if n has Property B， then 2n has Property B. It has been also proved that if n∈{2，3，4，5，6，7}， then n has property B[4-6]. In [7]， we proved that n=10 has Property B. In this paper， we will verify that n=8 has Property B.

Keywords：abelian group； zerosum subsequence； Property B

Similar to the proof of case 1， we can verify that there are at most two distinct elements in Tof case2 and case 3.

Theorem is true.

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（編輯：溫澤宇）endprint