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The Topologies on Cyclic Posets of Groups

LUO Shu-zhen1,ZENG Li-hua2,LAI Xin-xing1(1.Faculty of Science,Jiangxi University of Science and Technology,Ganzhou Jiangxi 341000,China; 2.Nanchang Campus,Jiangxi University of Science and Technology,Nanchang Jiangxi 330013,China)  
Based on the special structures of cyclic groups,the scott-subgroup topology σP(G) is introduced,and the relationshipes between the three differences topologies on cyclic groups are discussed,that is the cyclic topology O(G),the scott topology σ(G),the scott-subgroup topology σP(G).It is proved that if(G,O(G))is T0,compace space and sub(G)separate the points of groups G,then CO(G)=σ(G)=σP(G).
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