A Property on Minimal Zero-sum Subsequence in C8 C8

Abstract

We say a positive integer n has Property B if every minimal zero-sum subsequence of 2n － 1 elements in CnCn contains some elements n － 1 times． Property B is a central topic in zero-sum 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
• zero-sum subsequence
• property b