A Property on Minimal Zero-sumSubsequence in C8  C8

ZHANG Hai-yan; LIU Geng

doi:10.15938/j.jhust.2017.06.021

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A Property on Minimal Zero-sumSubsequence in C8 C8

更新时间：2026-08-31

- A Property on Minimal Zero-sumSubsequence in C8 C8
- Vol. 22, Issue 6, Pages: 113-115(2017)
- 作者机构：
  
  1. 1．哈尔滨理工大学应用数学系,黑龙江,哈尔滨,150080
  2. 2．哈尔滨理工大学荣成学院,黑龙江,哈尔滨,150080
- 作者简介：
- 基金信息：
- DOI：10.15938/j.jhust.2017.06.021
  CLC： O156．1
- Published：2017
- 稿件说明：
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ZHANG Hai-yan, LIU Geng. A Property on Minimal Zero-sumSubsequence in C8 C8[J]. 2017, 22(6): 113-115.
DOI：

ZHANG Hai-yan, LIU Geng. A Property on Minimal Zero-sumSubsequence in C8 C8[J]. 2017, 22(6): 113-115. DOI： 10.15938/j.jhust.2017.06.021.

摘要

如果在群CnCn中，每个含有2n － 1 个元素的极小零和序列中都包含一些阶数为n－ 1 的元素，那么我们称正整数n 具有性质B。在二维阿贝尔群的零和理论中，性质B 是一个中心议题。关于性质B 这一问题最早是由高维东教授和A． Geroldinger 提出并进行研究［1 － 3］。之后，他们证明了如果n 具有性质B［4 － 6］，当n 大于等于6 时，2n 也具有性质; 还证明了如果n∈{2，3，4，5，6，7}，n 具有性质B。在文［7］中，我们证明了n = 10 时，n 具有性质B。本文证明n = 8 时，n 也具有性质B。

Abstract

We say a positive integer n has Property B if every minimal zero-sum subsequence of 2n － 1elements in CnCn contains some elements n － 1 times． Property B is a central topic in zero-sum theory on abeliangroup 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 beenalso 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 PropertyB． In this paper，we will verify that n = 8 has Property B．

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