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G. Higman studied first the finite groups in which every element has prime power order except 1(see[1]),that is,the centralizer of every element is is a p-group except 1.Later manv authors have generalized it. On the one hand, the generalization is CN-groups, that is, the finite groups in which the centralizer of every element is nilpotent except 1(see[2,3]).On the other hand, the generalization is C22-groups, that is, the groups are of even order and the centralizer of any involution is a 2-group;a C22-group named again CIT-gro- 相似文献
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幂群与它的生成群 总被引:1,自引:0,他引:1
杨文泽 《数学的实践与认识》1998,(4)
设г是G上的幂群,即以G的非空子集为元素,在G的子集的运算之下所成的群.P_1,P_2是这样的两个性质 P_1:对任意g∈G,存g∈G,存在A∈г,使得g∈A. P_2:对任意A,B∈г,如果A≠B,则A∩B=φ. 本文得出了群G上的幂群г分别具有性质P_1或P_2的充要条件. 相似文献
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