摘要
讨论群的元素性质与群的根性之间的关系.考虑群的元素性质P满足条件(1):如果x是G的P-元素,且N G,那么xN是G/N的P-元素;满足条件(4):设N⊿G,如果x∈N是G的P-元素,那么x也是N的P-元素,则群类P1={G|G的每个同态像没有非平凡的P-元素}是P1-根群类.如果P满足条件(1)和条件(2),x∈N是N的P-元素,且N⊿G,那么x也是G的P-元素,则群类P2={G|G的每个非平凡的同态像有一个非平凡的次正规P-子群}是P2-根群类.如果性质P满足条件(1),(2)和(4),那么P,P2均为根群类且P=P2.
In this paper, we make a discussion of the relationship between the properties of the elements of groups and the radical properties of groups. If the properties p of the elements of groups satisfies the conditions （1） if x is p-element of group G and N G, then xN is p-element of group G/N, and （4） let N G, if x 6 N is p-element of group G ,the x is p-element of 5/,then the class of groups P1 = { G ｜ every image of G has not nontrivial p-elements} is p1-class of radical groups. If p satisfies the class of groups P2 = { G ｜ every nontrivial image of G has a nontrivial p- subnormal subgroup } is p2-class of radical groups. If p satisfies the conditions （1）, （2） and （4）, then p, p1 are class of radical of groups, and P = P1.
出处
《成都信息工程学院学报》
2010年第4期427-429,共3页
Journal of Chengdu University of Information Technology
基金
国家自然科学基金资助项目(10771180)
关键词
基础数学
代数学
群的根性
群的元素性质
由群的元素性质决定的群的根性
basic mathematics
algebra
radical properties of groups
properties of the elements of groups
radical properties of groups determined by properties of the elements of groups
