Minimal inner-Σ-Ω-groups and their applications  

作　　者：LI XianHua XU Yong 

机构地区：[1]School of Mathematical Science, Soochow University, Suzhou 215006, China

出　　处：《Science China Mathematics》2011年第9期1927-1936,共10页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.10871032);the Natural Science Foundation of Jiangsu Province (Grant No. BK2008156)

摘　　要：We introduce and study the minimal inner-Σ-Ω-groups and the minimal outer-Σ-■-groups.Then we give some applications and obtain some interesting results,including characterizations of nilpotent,supersolvable,solvable,and p-closed groups in terms of the join of two conjugate cyclic subgroups having the same property.We introduce and study the minimal inner-∑-Ω-groups and the minimal outer-∑-Ω-groups. Then we give some applications and obtain some interesting results, including characterizations of nilpotent, supersolvable, solvable, and p-closed groups in terms of the join of two conjugate cyclic subgroups having the same property.

关 键 词：nilpotent subgroup supersolvable subgroup a pair of conjugate subgroups minimal inner-∑-Ω- group 

分 类 号：O152.1[理学—数学]